An upper Tension assembly has no bearing on a treadle belt and visa versa. If your belt is slipping it needs to be tightened. Once a belt is installed, it could require tightening a couple to a few times, even if stretched beforehand. Room temperature can affect the belt. I demonstrated in an unheated cabin, opposite side of the cabin from the fireplace, by the second night, I felt the belt slipping.
I hope you get your machine running the way you want.