Diezmar has a diphthong because of diezmo, as the DLE says.
This could have happened by backformation and re-derivation: once you have diezmo, you remove the suffix -o that makes it a regular masculine noun and then add -ar to turn it into a verb. There's another verb that means the same, but the speakers don't like the fact that it has another root and forget it in favor of the one they've created.
Or it could be because of analogy: dezmar has several very common obviously related words and they all have a diphthong, so the verb changes to match the rest of the family. The noun diezmo was probably more common than the verb, and it was "backed up" by the extremely common numeral diez (and dieciséis, diecisiete, dieciocho, diecinueve). The only other form of this historical root that doesn't have the diphthong when stressed is décimo, but it is a bit technical and not nearly as common as the numerals.
In general one would expect that "irregular" vowel-alternating verbs would become regularized, as has happened in a few verbs like prestar and entregar (whose Latin roots had lax /ɛ/ and which had forms like priesto and entriego in Old Spanish).
There are however a few cases of regular verbs (with a Latin root in /e/) that actually took the other way and diphthongized, like sembrar and colar.
If you loosen the requirements a bit, you can find a lot of newer verbs that have a diphthong in all forms (that is, they don't alternate). However that's not because they've shifted from older alternating forms but because they were derived from nouns where the Latin root had a short (later lax) vowel which then turned into a diphthong. Since Spanish noun inflection never shifts the stress, nouns don't alternate vowels, so if a noun acquired the diphthong, it stayed there in every word that was derived from it.
So we have e. g. puente from Latin pŏntis, but the modern verb that means "to go over sthg./sbdy.; to make a direct connection in a circuit" is puentear, because it was formed on modern puente + -ear. In the same way there is fiestear < fiesta < Latin fĕsta (but festejar "to party, to celebrate* keeps the monophthong /e/ in the first syllable), and afiebrarse < fiebre < L. fĕbris (but we also have the somewhat cultured febril), and cuerdear < cuerda < L. chŏrda (but also cordón and cordaje).