Anya,
TyTy is a Georgia nursery with a horrid reputation. They have many spin-off companies (Aaron's) also selling the same plants. Their websites tend to look the same,etc.
Moving forward, I would recommend use the Dave's Garden link to research nurseries, check with the Better Business Bureau, but the easiest thing to do.....check here on the forum. You can use the search feature at the top of the page, and just type in "willis" for example, and see what comes up. This group is quite experienced, and we have had good and bad experiences with nurseries. Even when you purchase plants from big box stores you are at the mercy of their labelling system. Please know, there are NO stupid questions on this forum. You may get responses guiding you to posts where your question has already been addressed (that is why learning to use the SEARCH feature is so very important). It is a great forum, good people, a lot of knowledge.
I also like Edible Landscaping, Rolling River Nursery, Joe Morle @ FigTrees.net, and we cannot forget James Robin, Sr(JR) --call him 337-407-0188. If you order from JR he will ask you send him payment for the trees, and then in November he sends them to you and asks you to send him payment for the actual shipping after you receive your trees. He is in Louisiana, a good man---uses a lot of the funds from his fig tree sales to help care for his ailing wife. Many of us have purchased from him. He does not have computer business, just over phone. He is a hoot to talk to. And, I suspect he has the Celeste and the LSU Gold that you are seeking.