So, you moved the control to the opposite corner of where it used to be and turned it around? Couldn't just turn the machine around? Just picturing what you're doing here.
If my first guess is right, then yes, your machine will travel in all negative moves now since the coordinate system is still based upon the original corner (or original machine zero) and the signed directions. You could shift this and change the axis direction by parameters but you may have to change a lot of things if you've got tool changers, pallet changers, etc. Sounds like it would be simpler for you to use a G68 (coordinate rotate) command and the control will flip the code around 180°. So, based on your "new" part origin, you could type in the program a "G68X0Y0R180." A G69 at the end will cancel this.
Oh, and this is provided you have the G68 control option....
It's just a part..... cutter still goes round and round....