Yes, that's it, the semi-circular spanner with the single "tooth". It comes in many versions at different costs, and different degrees of quality.
I've found that the magazine-well vise block is vital when working on buffer tubes. Many tubes, even from the factory, can use a bit of tightening, along with some blue Loctite.
There seems to be a tendency for that castle nut to loosen a bit with extended firing. Seen in ultra-high-speed photography, all weapons "twang" when fired, which tends to mess with fasteners over time.
Proper procedure is to stake the castle nut to the back plate after tightening. I've seen it done only once, and that was on the Sig 556. I had it clamped properly into the vise, and even with the heavy duty wrench, I didn't think I'd get the castle nut off. It took the last bit of my strength to break the stake points loose. I'd hate to think what might have happened if I had a flimsier wrench, or a flimsier vise or vise block.
One final bit of trivial advice: beware of cross-threading the buffer tube into the back of the lower receiver. Both are aluminum, and threads can be messed up easily. When I have them apart, I used Nanolube on the castle nut, and run it up and down the entire length of the thread on the tube. Then more Nanolube on the tube threads, and screw it all the way in to the lower receiver. When done, you should feel no tight spots, and everything spins easily the entire length of the thread.
After that, you should still be extremely careful in threading these parts together. This is one job you want to get right the first time. That way you won't have any nagging doubts after you're done.