Are there two ways to say «μια»;

So, I speak Greek well enough that I can get by in most situations. I’m confused by something that happened recently and was hoping you all could shed some light.

The other day, I was trying to get into a sold-out restaurant in Athens with a friend. To make my case, I told the receptionist that we’d eat quickly and that ”Θα φύγουμε σε μια ωρα”. I pronounced “μια” as “myah” and he corrected m by repeating the phrase and pronouncing it as “mee-yah”.

The same thing happened when I told the server “Θα μοιραστούμε μια χωριάτικη σαλάτα”.

Is there a difference between the pronunciations? Is it a matter of “a/an” vs. “one”?