here comes the doctrinal debate of remission at repentance or remission at baptism...
Cornelius was spirit baptized before he was water baptized. Is it possible that his sins were remitted when he believed? Could it be that
Acts 10:43 means what it says? through his name whosoever believeth in him shall receive remission of sins. Would God put new wine (Holy Spirit) in an old bottle (unforgiven flesh still tarnished by sin)?
There are a lot of threads that touch on this already most recently Adino's thread on the Evolution of water/spirit new birth.