That was last Thurs...you won't get her till over a week later. You have no idea what disease or parasite she was exposed to in that week and could be incubating. In addition, just the stress of the move to a new home may bring on a URI that you would not want your other kitties exposed to.
In addition, shelters are typically understaffed, it's very easy for them to miss something, especially if it's in early stages. They don't get to spend enough time with the animals, the way an animal behaves in shelter is usually very different than the way they are when they get settled in at home. The vet was being paid to spay her, it's not likely that they'll do a full exam (Unless they told you he would), but even then, they are not likely to be as careful as when an owner brings in their pet. The first thing you should do when getting a new kitten is bring it to your vet to be checked out, before ever thinking of introducing it to any animals currently in the house.
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Holly, Misty & their friend, Jake, the dog.
Onyx, Callie May, Maggie & Kobi forever in my heart.
Yes, I know I need a new signature pic...someday...