They will probably continue to telegraph through the paint, you need to sand down until they disappear. For paint you don't need to get to bare wood necessarily, just a flat surface, the paint can fill the swirls.

The most common cause for this is skipping sandpaper grades in the sequence-- going from 80 to 150 without the 100/120 step in between. It can also happen if you use cheap sandpaper where the grit is not sized to a narrow range, sanding without a vacuum hooked up so that larger loose particles aren't sucked away, or just not sanding long enough. Occasionally there can be a problem with the sander with the mechanism that makes the orbit "random".

It's always a good idea to check the surface prior to finishing by dampening the surface with water or denatured alcohol-- any residual swirls will immediately stand out. The swirls expose end grain, which will suck up thinner or finish and stand out like a sore thumb. Water will also cause the grain to raise, allowing you to knock it off with a very light final sanding for a super-smooth surface.