When the back can move directionally as your has it is an indication that your basting is not taut enough.If you are basting with thread, try to make it even in each direction. I prefer spray basting very lightly and on some quilts, do anchor stitching in the ditch to keep the quilt square.If these are done with dissolvable thread, they are easily removed.
As for the tension, try adjusting on a practice sandwich before you get going on the quilt and you may have more success. All the best with the adjustments.
(Also make sure you have your quilt supported on a flat surface, and not dragging against you or hanging down from the machine).