The internal dimensions of the Thule Sonic XXL Rooftop Cargo Box, part # TH636S, which you referenced, measure 35-1/2" wide, so if your spare is 30 inches in diameter you should have no problem fitting it inside the Sonic XXL. (See included photo which includes all interior dimensions.) However, the tallest point internally is 15" and it slopes down toward the sides. You could have a fit problem there.
I have also included a video review of this cargo box for you to check out.
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The trailer hitch mounted cargo carrier is an outstanding accessory. It allowed us to bring so much more on vacation. The side rails made securing things really easy and the auxiliary taillight kit plugged right into my plug. The service was so great that I just ordered a trailer hitch cover for the winter. Thanks!