The rest of this part is simple. Follow the linear path through the sewers. There's no actual time constraint and the chase parts are scripted. Feel free to stop and break barrels, pick locks, and use dwarfnose.

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After the rockslide, just curve to the left and take the side route until you catch back up to them in the big room. After a little cutscene, one will be left behind to fight you. Move quickly, since he'll use throwing daggers until you get into melee. Break out a few strong abilities from Rhulana and Forgrimm to take him down. Then push further into the sewers.
Your next path is past the weak wooden wall. Break it down and go after them. You'll start running into wolf rats from this point onward. They shouldn't matter though, since you won't find any groups larger than about 4. Remember to go ahead and grab their tails. Keep going until you find another wooden wall. Break it down and look for dead wolf rats. The trail of dead bodies will led you toward the cultists. Go just a little bit further to find the big staircase and the exit.