You flew with Mokulele Airlines, which operates 9-seater Cessna caravans and does not require a TSA check. You landed at "Terminal 3" at HNL (in quotes since it is a trailer that is 1 1/2 miles from the main terminal and has no direct access to another airline). To continue on a connecting flight, you would have had to take a shuttle to the main terminal, where you would pass the TSA security checkpoint.
If you had flown Ohana Airlines, operated by Hawai & # 39; ian Air and using 49 seats ATR 42-500 from JHM to HNL, you would have gone through TSA security at JHM and arrived at HNL's main terminal without one additional TSA verification would be required Take a connecting flight, provided you either had hand baggage only or checked in to your final destination when you checked in at JHM.
You didn't notice the TSA checkpoint because it is only occupied when Ohana flights depart. These are 4 flights a day at 8:30 a.m., 10:30 a.m., 1:30 p.m. and 5:30 p.m.