Surviving the drones on the ground is actually up to your DPS killing spiderlings and you positing the drone correctly. Each spiderling that reaches your drone will buff it, and the buff stacks. Too many stacks = dead tank.
Logs will probably show your drone had many stacks.
But basically - park your drone in the corner to the left as you enter so spiderlings have the farthest to go. If DPS can't get the spiderlings down, you'll be in trouble, but you'll want to save your CDs to later on as the drone is getting closer to death and has more stacks. You may also want to call out for external CDs if avaialbe. However - make sure your DPS is slowing and AoE-ing the spiderlings effectively. If they aren't, you'll die 99 times out of 100.