"If you've got a problem with me then, come and talk to me, not anyone else."....not a good start.
To be fair, you MAY have misinterpreted the intentions there - I would also say to a student, that if they had a problem with something I had said or done (or NOT said/done) then I would like them to come straight to me, without delay, and address the situation. Certainly not go to somebody esle to complain. There's no need for that and it doesn't help anybody - often makes the problem bigger and may just be the result of a simple misunderstanding or honest mistake.
If a student has problems with me, as an individual, then I would be the first one to suggest they change to another instructor. They shouldn't battle on, if they're not happy. Back to that phrase of "You are the customer".