I keep having this problem while holding a tail press and going straight. The board always wants to turn. Sometimes, I can hold it straight, but most times, the board wants to turn. That means that my upper body isn't properly aligned but I just can't seem to figure it out. On flat ground, I can do it easily but soon as I take it to a mellow slope, it's either a hit or miss. Anyone had this problem while starting to tail press?
Need video to know what you're doing wrong, but here's a question, are you riding down the fall line of the slope? Typically if you're doing tail presses you want to be going straight downhill, in the same direction as the slope is slanting otherwise your board will want to turn and move towards the slant of the slope.
Also, the other big place people go wrong with their tailpresses is they try to lean back and lift their front foot up instead of shifting their bodyweight backwards and staying centered and balanced over their tail.
Kind of hard to help you without seeing video though, could be a million things you're doing wrong, but most likely you're drifting left/right because you aren't keeping your body centered over the tail of your board.