As others have said, everyone has a cleaning process that they like. When I tried TC#13 it was like rust in a bottle, at least for me. It might act as a surfactant when mixed with water, but I would not leave TC#13 full strength on blued steel.
I’m with the hot water crowd for deep cleaning blackpowder residue. We are on county water here, but use a whole house filter that is supposed to remove chlorine and other nasties. May explain why flash rust, even with hot water, is not a problem.
That is a good point; while the TC13 is quite effective at cleaning off the residue around the lock and nipple area, it WILL take the brown (or blue) off the barrel too. Gotta be careful.