it doesn't sound like your birds are having a lot of problems just your first bird would rather have it's own space and the newer bird is a bit more social. As they aren't having any major issues, with time, they will likely learn more toleration of the other. It seems like neither is very pushy.
If you didn't observe quarantine before introducing your new bid, you should have done that first, to safe guard any transmission of illness from your new bird to your old bird.
Also, if you just bought your new budgie home and put her straight in the cage with the male, this can also cause trouble. The budgies should be introduced in neutral territory (outside of the cage, if possible) and the cage where the male lived should have been rearranged before introducing the new female. This helps the older budgie from feeling too protective over what he considers 'his' space.
Depending on how long they've been together, you should consider removing the female for quarantine still.
Try to offer several perches and swings at the same height so that your male doesn't feel too pushed out, though to me it seems like the younger budgie is just looking for companionship from the older budgie and he doesn't always want it, but as long as he just hops away and that's it, there's nothing to be concerned about.