Hello: I am not aware that any of the typical insects that live on a holiday tree would be able to survive indoors for more than a short time. Fungus gnats (also known as drain flys) are associated with fungus and water(floor drains) and would not be found on the ceiling by nature and the water for the tree is to fresh and clean to support life. If there is a desire to put good ID to this insect and you can get a close up with a camera or smartphone, happy to take a look.
Psocids are a soft bodied winged insect and the only one of several that could hatch from and egg mass and leave the tree. Pscoids present NO danger and would not survive the hot dry air in a home. without a good ID, there would only be the one hatch.
Removal using a vacuum is the best method. Smashing them can leave a stain mark on the ceiling.