How does TIMP use port 8000 (and other ports)?

TIMP is composed by several applications that interact through COM and TCP/IP.
Port 8000, by default, is used to connect jpolld (which is the application that deals with client connections) to the main router.

Also port 8001 is needed for s2s (which is the application that deals with server-to-server connections) to the main router. Actually the Installation Wizard checks if port 8000 is available, if not it tries with an higher port number. Be aware that ports 8000/8001 must be open only for loopback connections (so, not in the corporate firewall, but in a personal firewall installed on the machine).

Ports 5222/5223 must be open in the corporate firewall to allow open/secure connections.

Port 5269 must be open in the corporate firewall to allow your server to interoperate with other public jabber server (a FQDN is also needed). If not open in the corporate firewall but only in the personal firewall, port 5269 allows various TIMP servers on different machines to interoperate.