My string loop knots keep twisting in opposite directions from each other after each shot....Why?

Hard to tell without seeing the knot.
Are you sure the knot is real tight on your string? Did you use some D-loop pliers, or needle nose to tighten the knot?

D loop pliers...

Alot of times it is the type of loop material used. It can also be caused by wax being in between the loop and the center serving or it can be the type of center serving on the bow. If it is tight, (and it should be considering you used a set of d loop pliers,) then it won't move up or down any, it will just be a little annoying for you to deal with while practicing. I wouldn't worry about it too much if you are confident that your loop isn't going to slip.