I've explored Mangar's Tower up to the spinning wheels on the wall and have looked at Mangar YouTube video but this quest is not markled as complete.

That pink circle sends me back to beginning and there's nothing new in Mangar's.

What am I missing?

It's hard to say what you are missing specifically.
When you finish Mangar's Tower you should have three teleporters that bring you back to the entrance area.
If you only have one, than you still have some way to go...

Yeah I explored it and only got one teleporter.

Will have to go back and start going through it all over again. Some of the puzzles in there are just infuriating.

There is after you kill the spectre the waves of skeletons to kill to complete the quest. Entrance is somewhere near the spectre .