I'm a bit confused about how TIJ works. If you're coming from the US and taking a domestic Mexican flight, don't you have to enter Mexico? So do they separate international and domestic departing passengers, or does everyone have to enter Mexico before they can fly out?
Mexico doesn't have any inbound immigration controls when crossing the land border from the US, so this is a non-issue.
Edit: Apparently they have a desk where you can buy some sort of tourist permit if you are going to be in Mexico for longer than 5 days, and there are reports that they are checking passports. If you want to avoid Mexican immigration, drive across at San Ysidro.
When you arrive from an international flight, can you skip Mexican immigration and just go into the US?
From what it says online, it appears that after baggage claim at TIJ, you can go straight into the tunnel without "entering" Mexico. TIJ doesn't have very many international flights, and there wouldn't really be much benefit to using this service instead of flying out of SAN or LAX. The real cost savings will be for flights within Mexico.
If it's just a foot border crossing, then yes ok the bridge leads directly into the main terminal, but no different in theory from going into Mexico via any other border crossing.
I believe it's just a foot border crossing, but it's privately funded and restricted to ticketed passengers, so you can get through US CBP in a matter of minutes, while the other border crossings would take hours. I think it's a waste of money going south, because you might as well just walk across any other border crossing and save the $16, but it would save you significant time going north.