1. Monster was summoned on player 1’s turn when exploring a Tile.
2. Monster set up but did not activate right away.
3. With players 1’s last action, he attacked the currently dormant monster.
4. Player 2’s turn: Resolve Impairments, then activate the monster player 1 summoned
5. Monster does all attacks.
6. Player 2 Does his actions.
What you've described in steps 4 and 5 isn't supposed to happen.
You only activate any given monster on one of the player's turns. A monster is associated with the player who sets it up on his or her turn. It only activates before that player's turn.