No, the Linux server is totally open. The problem is on my arbitrary Windows desktop machines, all of which run firewall software on them.
I believe what is happening is, after the tRio applet starts up, the tRio server sends additional data on another, arbitrary port, which of course the tRio applet can't receive, because of the firewall. So the server slowly cycles through all the ports on the machine until it finds an open one, about fifteen minutes later.
I've tried going through the source of the tRio software to see if there was a way to hardcode the port, but my Java is fairly rusty, and I know nothing about RMI.