Adding my thoughts a little to this. I find it really tough to break old habits of "doing the work" right then and there at the tactical meeting, because it used to be like that, and people have this feeling that if it can be resolved now why wait. It took time to adjust, and a lot of cynical eye rolling towards the facilitator when we first started
Periodically at the start of a tactical meeting, I would remind everyone that i would interrupt a discussion that goes on for more than a minute and will jot down a next action for it. This helps smooth out the process a little when I do interrupt.
When the tension bringer is satisfied, but someone still wants to continue the discussion, I would ask them if he/she would like to add the tension to the agenda so that we can have our fullest attention processing that at that point. If he/she says yes, then I'll ask the secretary to add the item and then move on.
Specifically about challenging the facilitator, I haven't experienced this, but I think I'd do what you did: ask the person to bring it as a separate tension anywhere, be it tactical or governance and let the process guide the resolution.