In previous Arabic lessons (a while ago, in 1957), I was taught to transliterate a kasra as an "i".
The internet agrees with me: "kasra (plural kasras): In Arabic script, the vowel point for "i", appearing as a small diagonal line placed below a letter ( ?? ) and designating a short i /i/. If the Arabic letter ?? (ya?) immediately follows, it indicates a long i /i?/. as an "I", not an "E", so you are inconsistent Furthermore, MY Syrian friend does transliterate his name as TAMIR (however, being a refugee--although a surgeon--he is not rich).
Interesting, but first of all I would say that we should not expect names to be rendered as strict transliterations in English (transliterations of proper names tend to have their own traditions – we write Lebanon and no-one complains). Then, I had a quick look at Tamers vs. Tamirs on Wikipedia; most Tamirs appear to be Israeli and most Tamers appear to be either Turkish or Egyptian (these two apparently from different roots).