I had a similar thing with Hondata on the FN2 with a different company.
During the mapping process, various maps are uploaded to the car during the live tuning process. If memory serves correctly you have to save the map on Kmanager and upload it into one of the two map slots and flash that to the ECU for the map to stay on the car after tuning. If the tuner doesn't do this, it will revert from the final map you see on the dyno to one of the temporary maps, which I'm guessing in your case is a map for tuning low cam since it only revs to 4k.
I found this out using Kmanager and looking at the map file, as it wasn't locked by the tuner. Phone conversation later and the penny dropped. If that does turn out to be the case, push for a refund as they haven't completed the work and get it mapped again locally.
The only other thing I can think it is would be a sensor fault which is making the ECU think the car is stationary, and the stationary rev cut which is about 4k, is coming in no matter whether you're moving or not.