They will trigger when a user logs in if they have met the default criteria for trophies which a few have been set up by default in XenForo.
Probably best to wait for another reply with better advice but I guess removing the trophies (make a back-up first, I think you can export them but I am using a modified trophy system so not sure if mine adds it or not) will make them stop working and remove the points for the existing users with these triggered.