If Angelsigh brought Katie to Olivers town, she'll appear in Olivers town at some point over the next three days, Angelsigh will get a gift from her in the mail as a thank you, and if Oliver takes her to someone's town when she appears he'll also get a gift. She'll stay in Olivers town for the whole day (6 am to 6 am) when she appears and will only leave if he takes her to someone else's town or if it rolls over to 6 am the following day, when she's in your town she'll just wander around the whole town randomly until you speak to her and agree to take her to another town.