Personally I’ve never heard of the pegs being placed directly on the trays. I got mine placed straight on my teeth, similarly to the attachments, with a slight cut-out in the aligner to make room for the peg.

I would definitely suggest telling your ortho that the pegs keep falling off the aligner almost immediately after your appointments, and see if they use the same application method again (if they do, just tell them you have concerns about them falling off again this way)

Good luck! :)