Learn English – Pronouncing “vis-à-vis”

It's not entirely clear what you are interested in.

With personal names (first and last name/surname), you pronounce it the way that person does. That's why you have to listen carefully when they introduce themselves. There's a lot of variation there. For example, I've met women whose name is TAmara (on the 1st syllable) and whose name is taMAra (on the 2nd syllable).

As for other proper nouns, such as place names and what not, there are dictionaries for that. The general rule is to try to get as close as possible to the original (foreign) pronunciation, applying rules of English phonetics.

This may be a more linguistic than ELL answer, but here goes:

(1) The stops t, p, k, when syllable-final, undergo glottal reinforcement in English. This minor glottal occlusion does not wholly impede the airstream. So, when the stop is released, the remainder of the air is released too. This is reminiscent of an unvoiced schwa, which accounts for what you hear after the t in cat. In terms of IPA transcription, one tends not to write the fine, automatic phonetic detail, and, so, for English, one marks only the preglottalization, as in [kʰæˀt].

(2) Crosslinguistically, the behaviour of syllable-final t, p, k varies. In Kiowa, for instance, as described by JP Harrington, t and p undergo complete glottal closure and are unreleased. In German, they are lightly post-aspirated. There are, however, only a certain number of perceptually distinct things you can do with your articulatory tract. So, my guess is, there'll be other languages that behave as English does.