Only reason why I got the alignment was because I replaced all four struts. The car has tracked great after the alignment. The pulling didn't start until they completely messed up the tire swap, this Saturday.
Right, but the car tracking straight could mean that the alignment had two bad angles that cancel each other out or minimize the effects until the tires change position. If that's the case then the bad alignment wear has already embedded itself into your tires. In your current experience, the angles longer able to cancel each other out because the two front tires are now on the left side of the car and the rears on the right side. I bet if you put the left tires back on the front/put all 4 tires back to where they were prior to your DT visit, the pulling will go away.
This happened to my cx5 after a firestone alignment. The toe angles were pretty high but they cancelled each other out until I rotated the tires, then the pulling happened. Sometimes done on track cars (intentionally) for some extra turn-in but you could only rotate the tires front/back and not diagonal.