You can add "to the teacher," but that is not necessary, and not the usual form. The other kid (and it is always kids who say this) usually knows from context who will be told. Also, kids will often just say, "I'm telling!" If there is a "to" used, it is usually "I'm telling the teacher" not "I'm telling on you to the teacher."

Synonym = to tattle https://learnersdictionary.com/definition/tattle

Yes, you have it right- if a kid "tells on" another kid, he's basically saying he will tell the teacher/principal about the bullying. *Just remember, this is for kids. You wouldn't say "if you do ___ I'll tell on you", as an adult haha. Pretty much, you shouldn't say this once you hit 13 or so :)

Hi Dani, thanks for your kind reply. Can it be followed by the preposition "to"? rell on him To someone

The meaning is correct - yes! I would personally say "Hey Chris, stop it! If you don't, I/we will tell on you"