The cURL library has a couple options called FRESH_CONNECT and FORBID_REUSE that help with special requests such as POST where responses often should not be stored.
However, I want to know if curl is smart enough to know a post/delete/put request with parameters should not be cached – or if these parameters must be explicitly set.
These options are related to the reuse of connections, not requests or responses. You can safely reuse a connection for multiple requests.