Internal Gear Hub Nexus 7

It sounds a little like you are shifting while pedaling. That's the opposite of how internal hubs work and will tend to cause the shift to happen delayed or never, and if done habitually for long enough is bad for the hub.

If you've got the yellow mark dialed and you're shifting only while coasting, and it's happening as you get into the slacker cable tension gears, it is possible there's a kink in the cable somewhere hidden by the housing, and it's causing friction that is making the shifting erratic.

I've had an Alfine hub, where the red/yellow lines weren't exactly right. I had to tighten the wire so it was just out of position, then shifting was much better.

Don't assume the mark is perfect, you may need to twiddle it to get the best-sounding changes.

I suggest you keep complaining to your dealer. Those Shimano gear hubs can be finnicky and quality control is not great - sometimes there is just a subtle manufacturing defect which causes bad shifting. For reference, I had a much more expensive Shimano hub replaced on warranty twice before I got one that worked properly.

But once correctly set up and if the hub is not defective, they should shift quite ok. The way to shift is to reduce pressure on the pedals, but keep pedaling, shift, wait until you feel the shift has happened, and then increase pressure on the pedals again. Pedaling backwards should not be necessary and could be bad for the hub.

The actual shifting is delayed a bit, the controls just tell the hub which gear it should shift to, and the actual shifting is delayed until the hub can shift. Usually (pedalling with little force) this should happen in a split second, otherwise you can sometimes hear the mechanism trying to shift but not succeeding.

I had a similar problem with a Nexus 8 hub where it would shift ok to upper gears, but sometimes it had problems downshifting to lighter gears. I discovered that my gear cable has a small fray that added some friction when downshifting.

As the bike is new, I would thoroughly check if the gear cable does not make tight turns, is well seated in the cable stops or has anything weird with it. If you don't find anything, I would replace the entire cable and casing because sometimes there is some bad cuts in the cable casing that adds friction that makes downshifting less precise or a terminal is rubbing with the cable. I would be a rather complex job to do at home and you would have to have some special tools, so I would recommend taking to the shop.