I think it is a limited slip and according to internet posts the Valvoline may not have enough friction modifier in it. Some state on the internet that adding more will smooth it out. The owners manual states to use Motorcraft 80W90 but thats like $25 a bottle on RockAuto. The owners manual does not state anything about friction modifier. So I simply went back to SuperTech which I used in the past with success. I do not feel any more vibration. I think most of these gear oils have the modifier in it and the Valvoline simply did not have enough. In any event I am satisfied with the SuperTech.
Simply do a google search of Valvoline 75W90 vibration and you will find one for the Tacoma and a Hyundai...and a few others.
This isnt too surprising. One time I used this Redline ATF for a 6F transmission thinking it would make the transmission more heavy duty. The Redline website said it would work...then after it was in the transmission felt very weird and sluggish. Its probably always best to use the exact fluid stated in the owners manual for maximum compatibility. Ultimately I had the 6F flushed at the dealership and it went back to smooth.