Differential fluids

Is it safe to fill both diff’s and transfer case oils until it oozes out from the fill plug?....just took my 2010 with 73k miles to the dealer to have it’s first drivetrain fluids changed and now I’m getting a “wua...wua...wua sound from my front end most noticeable from 20-40 MPH for the first 30mins of driving, once the oils heat up the noise is gone.
Sounds to me that they didn’t quite put enough fluid in there...any thoughts?...has anyone ever had this happen?
TIA

 

Yes, top the fluids off. Yes, stop going to the dealership, they frequently make mistakes.

 

Thanks
I’m trying to stay with the dealership because truck is still under warranty, should anything go wrong they can’t say that it’s because I didn’t take it to them for service

 

Damned if you do, damned if you don't!

You could take it to a different dealership and tell them the diff is making noise, they might give you a new one

 

LOL.....this truck is in awesome original condition, don’t want anything touched or replaced unless absolutely necessary.
Purchased this in Oct. 2019 with 60k on it from the original owner.