So you are telling me that the universal translator is ALWAYS active and they just don't mention it most times? It's built into both ship comms and individual communicators and in most cases it 100% suppresses the original spoken language audio and makes the alien's lips visual sync to spoken English?
They don't mention it because it would get annoying if they mentioned it every episode. The translators 100% suppress the original spoken language so that the viewing experience is not horrible. The actors/actresses lips visually sync to spoken English because if they didn't, it would look ridiculous. Imagine how annoying it would be if almost every character (even the main characters, since Picard likely spoke French) did not appear to be saying what they were saying.
The reason everyone speaks English is because of Universal Translators that translate every language into your own. There are some rare times when Universal Translators don’t work, also for some reason Klingon never gets translated into English.