SIP Port Clarification

As long as there is only 1 phone at the remote location it's pretty basic. It will register using port 5060 and this will open a state on both firewalls. Once the phone has registered and the state is open on the home router, than it is as if port 5060 was open on the home router as well. It will let incoming connections from the trixbox's public IP in and forward them to the NAT'd phone because it matches the open state.
If there were multiple phones connected behind NAT, all using port 5060 to register, then it would be more complicated because several states would match an incoming packet from the trixbox IP on port 5060, so the home router would not know which device to send it to.
In short it works because stateful firewalls are designed to allow traffic to flow both ways once a state has been opened between local endpoint and distant server. Otherwise you would not be able to browse the web or do anything on the internet without opening ports on the firewall...

5066 is the local sip port on the phone. It will still register to port 5060 on the server. It will tell the server to send SIP requests on port 5066.
Traffic will go like this:

asterisk:5060 internet home router:5066 sip phone:5066
The phone is sending requests out to port 5060 on the trixbox IP. It is listening on port 5066 for SIP messages.
The asterisk server is listening on port 5060 for SIP messages. It knows to send SIP messages out on port 5066 to that remote phone because it registered accordingly.