Kleene's Theorem and TMs

I wanted to know that based on Kleene's theorem (a language is regular iff some FSA recognizes it), does every regex have a TM (Turing machine) that halts on exactly the same language?

Is this implication valid or are we not entirely sure about this? (ambiguous/unclear given the theorem). Kind of like the Church-Turing thesis about computation in the future and all computation in general.

Theorem: A language $$L$$ is regular if and only if there exists a DFA or NFA for language $$L$$.