Maybe I was experiencing a bug, because standing ontop of a raid member allowed me to do damage to them (thus boosting my DPS as well).
The "cloud" does 2 things:
First it deals damage to you every few seconds... something like 3-4k per tick.
Second, each of your attacks deal somewhere between 2-3k per tick on your target.
I accidentally picked up the cloud when moving to kill a beacon so that's how I know. It doesn't deal damage to people around me because no one else took damage when I was stacked with the group.
One of the reasons you want to the tank to pick it up is because it makes it easier for healers because the tanks are really the only ones who are supposed to take damage during that phase (exception to ranged DPS for slimes). But also because it helps them with threat because of the +2-3K damage they deal because from what I can tell, holding threat on the Tunneling Tentacles is quite exhausting.