I have found they need to enter the room I completed, before I enter the next room.
But I have had runs where I just blazed through and never felt the loss of items even if they weren’t all perfectly in sync. And runs where I felt like there was no bonus when I did this even after letting them catch up until they were caught up for a couple of rooms.
It’s fucking weird.
So keep em all as close as possible and let the divs rain. Find trusted people to add as friends so they don’t have to stay out. 🤷♂️ or be a trust worthy leecher who keeps up so runners will invite you back.