I don't think this behaviour is a problem, but it is inevitable if you use cookies to store the session id. So if you really must avoid this behaviour, pass the session id in urls instead of cookies.

As a start, in your cgiapp_init you would need to avoid sending cookies:

 $self->session_config(
          CGI_SESSION_OPTIONS => [ 
           # whatever
          ], 
          SEND_COOKIE         => 0, # defualt is 1
 );
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Next you'll have to arrange for all your urls to contain the session id (and you will learn much while contemplating how to do that).