1. Is the trigger which you're using an event trigger or a box/poly trigger?
If it's an event trigger, that's normal:
As I explained above, triggers throw enter and leave events for any character for which they are registered.
Event triggers are always registered for all characters.
Box and poly triggers need to be registered for those characters, whose entering that trigger is of interest to you.
If the characters of interest are players, it is better to use ProcTriggerRegisterForPlayers because simply using TriggerRegisterForPlayers will keep that trigger registered for characters which are currently players but later become NPCs and will not register it for characters who are currently NPCS but later become players.
2. If it's a box/poly trigger, can you post whatever code you're using to register these events here?