I have always played this as "no" because the warrior was not in the capital city when the group ally card was drawn. In my games, when someone has the horn, one more more other heroes are low on health, and we know that a group ally card is coming up, then we use it on that player's action in a previous turn so we can all start out in the capital when that group ally card is drawn.
Learning the turn deck this way is the major part of the strategy of TED.
This is correct. The start of the turn is when the ally or group ally card is drawn. With group ally, it starts the turn for everyone at the same time.