How much time or distance did you drive between when you think the leak started and when you stopped for the tow? I'd expect some transmission damage. A shop can remove the transmission sump pan and look for shiny bits of metal, or just a fluid drain will bring out some. These are debris from damage.
I think you need a fluid labeled for Toyota type T-IV, but check this. If you were sold the wrong fluid, that may contribute to the poor operation.
So--consider the wrong fluid level, or the wrong fluid, or damage. Do drain out some fluid and look for bits of metal in the fluid. If the fluid is clean but you put in the wrong stuff, do a complete fluid exchange with the correct fluid. I'd always put a Magnefine-type filter in the line to the cooler.