What you are seeing might be normal, the frequency counter feature on your scope isn’t going to be as accurate as a dedicated Frequency counter.
If you think the Frequency is really jumping around then don’t look at the trigger position on the scope. What you should do is adjust the Horizon position so that you are looking at the waves a lot later than the trigger position (I.e. the trigger position disappears off to the left of the screen). Then set the display to Infinite Persist. With your scope setup like this any frequency changes between the trigger position and the position displayed on the scope will cause the waveform to be drawn in a different position on the screen, and since the scope is set to infinite persistence you will see it. So you can leave the system running like this for a while and if the frequency is really jumping you should catch it.
Remember you can test the principle by manually changing the Frequency of your function generator by a small amount temporally.