How do split panes in Terminal work?
It's meant to be like that. See this Super User answer:


  You're misinterpreting the feature. It's not meant for two separate
  terminals. It's intended to allow a
  user to see two different view points
  in the same terminal. For instance, if
  you have 3000 files in a directory,
  and you perform an ls command, that
  output is going to be very long.
  
  If you use the split pane, you can
  scroll through that long output
  without having to flip back and forth,
  possibly losing your place along the
  way.
  
  If you want two terminals, use tabs,
  or separate windows.


I would add that, for two separate terminals, you can use separate tabs as well.