When playing 2-player co-op, the monsters that drop the red AOE under players has been invisible to the person who wasn't hosting. When I hosted, the person I was playing with couldn't see them (but I could) and when someone else hosted, I couldn't see them (but they could).

I received my copy from twitch drops if that matters.  In the first example where I hosted I was playing with someone who had the twitch drop as well.  When I played as the person not hosting, the host had purchased the Last Wish edition (in case this matters).

I played a total of five 2-play co-op games and it was true for all 5 games.

Edit:  The indicators for all boss attacks were visible to all players.

Temporary Files.7z

Steam_0x0110000102d32216_01.ctr