glue

Hoping I can get some insight here. I've watched many build videos and have noticed many, if not all, seem to be gluing parts in right over painted parts. When I do this, it turns into a gooey mess. What am I missing? Grateful for any help.

I've got a Revell Type XXI submarine with interior I'm working on putting lights into. I bought these 1mm LEDs pre-soldered to what look like 30 something gauge wires. The LEDs themselves adhere easily enough to the plastic with CA glue and some the stuff you can use to speed up the curing time...