When the tester has a different color than the perfume

No, I never noticed a colour change in the bottle that I just bought.

Some perfumes get flocculations when they are aging.It happened with my Bois d'Armenie (app. 3 years after purchase). I do own an old Joop!Homme from the early 90ies that has become grey instead of pink.

It happened to us: Penhaligon's Love Potion No 9 - it turned from nice dark violet to earthy-red + in the shop where a bottle also almost in brown color, and there were two reasons:
- for our bottle, that it got canker
- in the shop, that it got too much sunshine.

Seeing as many testers get left out under store lights all day, I'd say it's light damage. However I don't assume that light damage is always bad. Who's to say? Just too many variables.