To use a pet stone you need to summon the pet, target it then click on the stone.
Assuming the stone is a Flawless stone then the pet in question will go from what ever quality to Rare.
This sort of thing takes some faith on the traders part, since the stones are no trade you have to trade a pet to the person with the stone. So pets you can not cage don't work.
Just be a bit careful with hard to come by pets. Vendor bought are about the only thing I would risk on this sort of venture.
Personally I would say Sffcorgi is not out to rip off people, so I would trust her/him(sorry I suck at guessing gender) if I was in need of this service.
I tend to take into factors like when they signed up their account on WCP, what their pet collection looks like, have a linked armory account and even how often they post. Someone with a new account, 2 posts and no pet collection uploaded would send up red flags for me.