If you rent a VPS, you’re having a legally binding contract with whatever company you choose. Read that contract/agreement! It will contain information like if they snoop at your data, if you allow them to rat you out to somebody else or what is allowed and what isn’t allowed and consequences if either party does something wrong. You won’t find that specific information in US law or some general answer that applies to every provider.
If they say in their TOS: ‘we will ban you if you do X’ and you agree to that and then do X, they’ll probably ban you… if they say something else in their TOS, then something else will happen. this is how contracts work.
However, i’m not sure if US law provides citizens with something like privacy. In other jurisdictions, it is forbidden to just scan through all your customer’s data to see if you can find something incriminating. At least on the level of pirating some movies.
And the FBI might have real criminals to arrest. I’m not sure if they’re actively looking for peanuts like one person who runs JDownloader. Unless you point them right at it. YMMV