My apologies if this has been asked before.

When spectating a match in the Cup, I noticed it went to extra time, and then in extra time each team scored once. Then, it seems like by the away goals rule, the away team that scored in extra time moved on, and the home team was eliminated, rather than going to penalties. My question is, has this always been the case? And doesn't this give an advantage to the team that is away for the second leg, even though it's essentially luck of the draw who hosts the first leg? Thanks all!