Just an observation - where I live, the distinction in speech between a mobile phone and the ordinary type is dying out. Hardly anyone says "cell phone" or "mobile phone", and if they say "smartphone" they're not referring to the device in its making-phone-calls capacity. So just "phone" shouldn't NECESSARILY be accepted here, as this could be just a dialect thing, but that's what I'd naturally use in speech to express the concept.
You have question marks, but it's not obvious what your question is. Are you asking why that answer was accepted or asking why it wasn't accepted?
"his mobile phone is at me" is a very literal translation of "tá a fhón póca agam". In fact, it's an overly literal translation - when someone says "Tá X agam" in Irish, they almost always mean mean "I have X", and Duolingo would be doing you an injustice to suggest that "his mobile phone is at me" is an acceptable translation of "tá a fhón póca agam".
Irish never uses a t-prefix to separate two vowels - a t-prefix almost always follows an, which does not end in a vowel.
An n- prefix sometimes occurs between two vowels, but it is not done to separate the vowels, as it is also inserted when the previous word doesn't end in a vowel - ár n-athair - "our father", bhur n-athair - "your (plural) father", a n-athair - "their father"
A h-prefix is sometimes used in positions where the previous word ends in a vowel, so you could say that it is used for the purpose of separating two vowels, but there is no general rule that vowels have to be separated by a consonant.