After completing our first level 90 monolith with me as the host, only I got the harbinger eye drop and unlocked empowered timelines. My friend had enough stability to start all of the monolith boss fights on his own and we completed multiple lvl 90 monos together without him unlocking empowered. We did all monos twice, once with me starting the echoes and boss quests and again with him starting the echoes and boss quests, still no unlock.
This has happened on two sets of new characters where only i unlock empowered monoliths and he doesn’t.
It shouldn’t matter who is host. If we grind out every single monolith together in the same lobby we need to experience the same level of progression, key item drops, and empowered monolith unlock