Well - if on a three speed Brommi your Gears are jumping it is amost 100% sure that the shifter cable needs a tiny bit of adjustment. These three speed hubs have been on the market from various brands for roughly 100 years now and so has the way of adjusting them. The video that you found explains it pretty well. What you do is to screw the nut at the end of the gearcable that goes onto the little chain a tiny bit and probably that's about it. Takes 10 seconds or less. If you grew up with these kind of IGHs (as I did) you do possibly not follow the official path but what the guy in the video outlines is one of the official ways.

Second gear, look through the hole on the axle nut, see the chain. Adjust the nut mentioned earlier bit by bit until you can see the in the hole the bolt that is on the other end of the tiny chain looking into the hole for about 1mm. In theory it should work now. In practice it may or may not but it is really easy to adjust these hubs: They have three gears in a straight line and one single possiblity for adjustment which is tightening or loosening the cable (in your case possibly tightening just a tiny bit). If they work they work, if they don't they don't. In this case play with the nut until they work. That's about it. If that sounds too complicated you should better go for the dealer.