Yes, οι,υι,ει,η,ι,υ all have the same sound. It would be "αυτή τρώει", though.
I just did 2 exercises that mentioned "ρύζι", one pronounced it as Z and the other one as "he" (as in He, She, It). Which is the correct pronunciation???
With a Z (http://el.thefreedictionary.com/%CF%81%CF%8D%CE%B6%CE%B9), the TTS audio is bad.