Why do I hear a "t" between each word and something like jaydatan and not jayda?
The whole audio is wrong in fact.
Correct pronunciation should be: Sámiyah mutarjimatun jayyidatun.
The "T" sound you hear is the result of Ta-Marbuta ة which is mostly a marker for feminine nouns and adjectives. This letter acts as "H" when the word is isolate or when the word is at the end of the sentence. However, when the word must be declined (i.e. the vowel on the last letter must change according to the status of the word) then this H changes to T.