Tener -> ten (tú), tené (vos, southern cone), tenga (usted, third person)
Decir -> di (tú), decí (vos), diga (usted)
Decir in present tense second and third (usted is the same as él/ella/eso from now on each time I conjugate in third person I also do in the second, to clarify what I think is a confusion of expectation with categories misplaced) person singular, so:
Decir -> dices (tú), decís (vos), dice (usted)
Se second part about added prefixes I didn't get, do you mean the added suffix pronoun? like from decir, dílo, or tener, ténlo. (you used the diacritic, in Spanish we use diacritic for one syllable words to specifically distinguish it from same sounding one syllable words, quite useful, from where I deduce that is what you mean when referring to the derived from "tener".
Also, this derivations are "conjugations" not "verbs", since it's the same verb used in different ways, even the mood changing might look like verb changing for very irregular verbs.
The table is incomplete, or at least misleading, mixing English and Spanish in some boxes, and some like predict is just as if it were in English as a comparison with "predecir" in Spanish, which its conjugated like "decir" one of the highly irregular ones, the word is simply an attached prefix pre- to decir. Much like how you would conjugate "contradecir" (contradict literally).
Lemme go on a limp and assume you are an English speaker, and try to fill in the gaps of what I understood is your question so if it isn't don't even bother reading my attempt at answering since it would be meaningless.
So English is your thinking and dreaming language; in Spanglish, thinking with both ways they treat the verb morphology or shape, the chart makes sense for one who is fluid in Spanish also, more than a chart of what people use to study, or synthesize ideas.
Your chart seems like a chart of the thought direction and orientation of yours when thinking of this problem (vs. organized for anyone to understand), and you got confused with the third person imperative and present tense in the third person: because there are no "present" imperative, imperative has only it's default "tense". when using with a pronoun it goes as a suffix always, with tener ending in -lo/s -le/s -la/s depending on gender and number, so third person imperative ténlo (tú), tenélo (vos), Téngalo (usted). I hope I got the gist of your question, I guess your not even wrong, but conflated expectations where there was no hope in the first place to predict or divine this things (conjugations).
I have to say what I always hate being said to me: "Rules are necessary, deal with it, it's what people do", you won't understand it because there's no correspondence. You'll only get to know this and use this by heart, there's no mnemonic device that quick, reasoning or logic to the highly irregular verbs, which aren't many. All new verbs like googlear (to google) are rational, follow rules you can learn or memorize. Tiene is indeed the third person singular but it's not the imperative mood of the verb, it's the indicative mood (most common one, I'm just used it now). with "decir" you got it right! and both are irregular, it's just that what is affected b "irregularity" is far broader in some languages than others, for example in English, the conjugation chart to differentiate regular from irregular verbs is as simple 2 entry chart of each verb and the indicative mood of the present tense, past and past participle.
In Spanish the irregularity of those verbs, and there are handful only that have this level of morphing, change and custom, one ends up learning this by heart (no logic to it): ser is the worst to learn, and the paradigmatic example of an irregular verb.
Like in English, we have regular and irregular verbs in Spanish also. Unlike English, most Romance languages have pronominal verbs, where it is accompanied by a reflexive pronoun before/after or as a suffix;
Tener is one these. Highly irregular but not as irregular as "ser" but a little more confusing/harder to remember than "satisfacer".
