Could that be mold and not water stains?

What primer did you use before adding the drywall mud?

About the only primer that will stop old water stains from bleeding thru is shellac. Zinsser's Bin primer; the one in the red can is a pigmented shellac. If you used any primer other than shellac, the discoloration is almost certainly because the old stain has leached through the primer and the mud.

I used Kilz all purpose. I am going to try the Zinsser’s Bin primer like you recommend and I hope that takes care of it! Thank you so much!

Make sure that you get the original shellac and use two coats, allowing it to dry between coats. It's available in spray cans which would be less messy. I'd probably use three coats if using the spray. (Zinsser has a synthetic shellac. I have not used the synthetic version. Would stick w/ the original, tried & true, formula.)

It worked! The ceiling is beautiful! Thank you so much for your advice!