Built a Creeper farm with trident killer and wanted to watch to see how fast creepers would spawn. I then used the command /gamemode spectator then flew into the wall to watch the creepers land in trident killer and realized they stopped dying. As soon as I used the same command to go back to creative they started to be killed again. (Use pigman spawner in video because spawn rate is faster)
Tridents thrown into a trident killer belong to the player who threw them and deal damage as projectiles of that player. In spectator mode they should be expected to behave the same as arrows shot by the player in spectator mode.
If you want to observe your trident killer in spectator mode it may work to shoot the tridents out of a dispenser into the trident killer.