ᴛᴏᴏ ʟᴏɴɢ, ᴅɪᴅɴ’ᴛ ʀᴇᴀᴅ
The short story is that Spanish speakers’ habit of pronouncing English yellow like jello is not about the region but rather about what happens to that sound whenever it shows up at the very start of an utterance, or after an ‹n› or ‹l›. Despite appearances, this is actually unrelated to how all of Mexico treats words spelled with ‹ll› in the same way as they treat words spelled with ‹y›.
All About Affrication and Yeísmo
I’m afraid that your question is just like asking which parts of the United States pronounce “did you” as “didja”. It’s not really a regional thing so much as it is one conditioned by other factors.
Unfortunately, whoever suggested that you pronounce the ‹ll› in Spanish tortilla like the ‹y› from English yes was at best presenting you with an off-the-cuff approximation just to get you started. The actual Spanish sound isn’t usually precisely like the English one, but the way it differs isn’t something your ears will be attuned to as an English speaker.
We have to use the International Phonetic Alphabet to talk about sounds, because we can’t do so using letters from the English alphabet. The IPA has a one-to-one correspondence between each written letter and each spoken sound, but the English language quite notoriously does not. So I’ll often use IPA for the pronunciations below since otherwise we just don’t have the “vocabulary” to discuss this, and I’d risk confusing you as badly as your earlier instructor has done. These are small differences, but until they happen in your mouth without thinking, you’ll always sound like you have a heavy, foreign accent.
I mention this up front because the sound you spell with the letter ‹y› in English is in the International Phonetic Alphabet spelled [j], whereas the letter ‹j› in English is spelled [d͡ʒ] in IPA (and the tie mark above the two letters [dj] is often omitted). So for example:
In answering why a native Spanish speaker would pronounce the English word yellow so that it sounds like the English word jello to you, we have to go beyond any regional pronunciation and discuss certain general phonetic characteristics of the language because what you’re hearing is about the language’s overall phonology, not about any particular region.
One of the most important factors that bring out what you’ve called “the J sound” is when a word beginning with the sound you’ve asked about is the very first (or only) word in the sentence. If you asked who wanted ice cream and somebody speaks up and says “¡Yo!” emphatically, that word can easily come out sounding more like the start of the English word judge than the one at the start of the English word yes.
Because a single word spoken in isolation is pronounced in an emphatic way, it can be difficult to get a native Spanish speaker to say the English word yellow in a way that doesn’t sound to you like they’re saying the English word jello, or the word Yale (meaning the university) in a way that doesn't sound like the English word jail.
Although to you these are two different sounds altogether, to a native Spanish speaker the two sounds are interchangeable variants (we call these allophones) of the same underlying phoneme. You can swap those sounds without changing which word they perceive was spoken. It’s phonemes that determine which word it is, not allophones.
The sound at the start of English yes is an unstable one, and not just in Spanish, which is why English speakers normally say didja when speaking did you quickly or casually. Phoneticist sometimes refer to this sound as yod, and it is responsible for a great many of the characteristic changes to Spanish spelling and pronunciation compared with Latin. The fundamental instability of the so-called “yod” sound accounts for the many new diphthongs in Spanish compared with Latin. It’s also responsible for the Spanish spellings ‹ñ› and ‹ll›.
The fancy word phoneticists use for the sorts of consonant sounds like the start of English cheek or judge is called affrication. You’re apt to hear an affricated sound in the Spanish words inyección and inyectar because there the ‹y› follows a written ‹l›, and in the Spanish words enyesar and cónyuge where it follows a written ‹n›. As far as I know, this is as common in Mexico as it is in Spain. You hear it all the time and think nothing of it. It’s something that “just happens” normally in the way that did you coming out as didja in English just happens naturally.
That affrication is also quite common at the start of words starting with the yod sound when they occur right after a word ending with the letters ‹n› or ‹l›, such as in el yogur, el hielo, en hierba/yerba, el yelmo, en hiedra/yedra, el yeti, con yema, el yeísmo, un yeísta.
Even those native speakers who do not pronounce a written ‹ll› as though it were written ‹y› normally affricate their ‹y› sounds in these scenarios.
That phenomenon is not limited to the yeístas described immediately below. Rather, it’s common in all speakers independent of their regional accent. If you ask them why they’re affricating that sound, they might think about it a bit and tell you that it’s just a bit too hard to say otherwise. Yes, they can make an unaffricated version when speaking very carefully and slowly, but it’s easier to turn it into the affricated version you’ve described.
On yeísmo and yeístas
The reason you were taught to pronounce the ‹ll› in Spanish tortilla as though it were spelled with a ‹y› is because all of Mexico is a yeísta region. That means they all say [toɾˈtiʝa] not [toɾˈtiʎa] for that word. The latter pronunciation does still occur in a few regions other than Mexico, but it has nonetheless become a minority use by overall numbers.
In fancier terms, Mexican Spanish speakers have all merged the palatal lateral approximant phoneme /ʎ/ into the voiced palatal approximant phoneme /ʝ̞/. It doesn’t work that way for all possible native Spanish speakers, as the linked article explains, but yeísmo is extremely common throughout the world, and no one will think anything at all if you’re a yeísta speaker.
Even when this sound is only an approximant, the Spanish sound [ʝ̞] is “thicker” than the English sound at the start of yes, /jɛs/. When it’s a fricative it’s decidedly “thicker”, even in some speakers and utterances varying from [ʝ] to the [ʒ] sound of English leisure, especially in the Rioplatense dialects of South America. And in emphatic positions, the /ʝ/ phoneme becomes not just fricative but affricated, rather like the two instances in the English word judge.
I’ve said “rather like” not “just like” because the English afficate is [d͡ʒ] but the Spanish one is normally transcribed as [ɟ͡ʝ] there.
Phonemes versus allophones
The important thing to understand is that these sounds are all valid phonetic realizations of the abstract phoneme /ʝ/, no matter whether that’s [ʝ̞] or [ʝ̞] or [ɟ͡ʝ] or [d͡ʒ] or [ʒ] or [ʃ]. We call the different ways to say the same thing allophones. Those all mean the same thing no matter how they’re said, and how they’re said varies far too much to give you some sort of “rule” that says that this or that region of Mexico uses one or the other. It doesn’t.
Instead, this is more like did you versus didja in English. You can’t pin it down to a region because it doesn’t work that way. Some speakers do it more or less than others habitually. Others do so only when it’s emphatic.
You can get a general understanding of how this all works by reading
material in English, but for the most accurate and nuanced treatment
you will need to read about it in Spanish. For example, from
this Wikipedia page
we learn that:
Ya desde mediados del siglo XX comenzó la pérdida de /ʎ/ (ll) en la
mayor parte de dialectos del español en favor de /ʝ̞/ (y). A día
de hoy, el fonema lateral /ʎ/ se puede considerar como prácticamente
perdido en los mayores dialectos del español.
Este proceso se trata de
la deslateralización de /ʎ/, conocido más ampliamente como yeísmo;
pollo [ˈpo̞ʝ̞o̞] y poyo [ˈpo̞ʝ̞o̞]. La distinción de estos
fonemas subsiste solamente en el español paraguayo, el andino, algunas
zonas rurales de Castilla y León, Castilla-La Mancha, Aragón, Murcia,
Ñuble, así como en los hablantes bilingües de español y catalán,
gallego, quechua, aimara y otras lenguas; poyo [ˈpo̞ʝ̞o̞] y pollo
[ˈpo̞ʎo̞]. El fenómeno opuesto al yeísmo, lleísmo (neutralizar
/ʝ̞/ y /ʎ/ en /ʎ/), también puede darse escasamente donde se
distingue /ʝ̞/ y /ʎ/; pollo [ˈpo̞ʎo̞] y poyo [ˈpo̞ʎo̞].
/ʝ̞/ se vuelve la africada [ɟ͡ʝ] o su variante dialectal y enfática
[ʤ] en principio absoluto de palabra y tras el archifonema /N/; enyesar
[ẽ̞ɲɟ͡ʝe̞ˈsa̠ɾ]~[ẽ̞nʲʤe̞ˈsa̠ɾ], ¡yo! [ʤo̞].
En el español rioplatense, del entorno de Buenos Aires y otras zonas de
Argentina y Uruguay, no se da la presencia de /ʝ̞/ ni /ʎ/, mas sí
se da un yeísmo con rehilamiento ([ʒ] o [ʃ]), zheísmo y sheísmo;
pollo [ˈpo̞ʒo̞]~[ˈpo̞ʃo̞] y poyo [ˈpo̞ʒo̞]~[ˈpo̞ʃo̞].
Please see also this related answer for a broad overview.