How old is it?
Make sure rear wheels are attached correctly and the pumps are not loose from the frame. Make sure frame has no cracks.
Has the hydraulic fluid ever been changed with a new filter?
0 turns are sensitive. Took me a while to adjust to using one. If older, there is a shock absorber on the linkage somewhere that helps stabilize movement. Make sure that isn't worn out.
Make sure the linkages do not have any slack. A 1/8" slack will let the handle move 2".
If the fluid hasn't been changed, there may be water in it and the wandering could be when water hits the pump. (Wild guess) I am not sure what else would cause the controls to act like that.