Min-raises preflop can mean very different things for different players. Some players will play their strongest hands like this e.g. AA, KK, QQ. For some players it means a mediocre hand who either want to see the flop or next card cheap.

You are best off avoiding calling min-raises preflop unless you have a decent hand. For example 77 and you calling for set value. If you have a strong hand (for example TT - AA) you want to reraise these guys and get an idea of what they are holding. An AI bet here usually means AA or KK or sometimes AK from opponents who are unsure of how to play AK after the flop.

ATF these bets are usually one of two things; your opponent is on a draw and wants to see the next card cheap, or has hit something on the flop but doesn't know how it holds up against your hand. It you have a legit hand you will probably want to reraise your opponent (after considering your position) making sure you are not giving them the drawing odds.