Every website you visit places a cookie on your computer, it lets other websites know what websites you frequent so they can place ads appropriately. You ever do a search for something like cars or chinese food and suddenly the only ads you see online are for cars and chinese food? This is cookies working in action. Ever see your password filled in automatically? This is because your password is saved in your forms list. Ever seen a webpage load suspiciously fast? It's because the html is already saved(cached) in your browser.
So simply, delete all cookies, forms, and cached webpages, and browse through https both before and after you visit JTF, and you shouldnt raise any flags. That being said, using someone elses internet is FUNDEMENTALLY insecure, but someone would noy try or care to see what you are doing unless they have a personal grudge against you and 2+ years in IT to back it up.