First tell clearly - problems and what are you trying do. You never said you are doing TSPITR.

1. Same database - You need to Shutdown database, Mount and Complete restore and recover until time. You cannot do TSPITR here.
2. TSPITR to a different database ( know as Auxiliary DB), just for a tablespace. As Devy said, steps are different. See the document.
http://download-uk.oracle.com/docs/c...1/rcmtspit.htm