a picture would be helpful, painting a stripe all around the room does not compute

I'll bet another coat would do the trick. I patched a hole in the drywall in my family room before painting. The patched area had a slightly different color after the first coat; after the second coat, I can't find the patched area.

Painting over it wont hide the tape. You need to have someone feather mud out farther so the tape isnt noticeable or have someone put texture on the walls. They did a bad job taping/mudding. Why did they say wait a year to paint? No reason for that. Probably so you wouldnt notice the tape within warranty period.

I agree it's a drywall issue, but don't forget the higher the shine, the more pronounced your bad drywall will be. Satin is too shiny for walls in my opinion. Eggshell or a low lustre would be more appropriate.

flat or matte would be better yet