I believe you are pretty observant. Mine shifted pretty much as you described. I think the clutches need to break in because after about 50 miles mine shifted completely different. I enjoy shifting manual and speed control with the throttle is excellent.
There is a clutch adjustment and the service guy told me that the adjustment procedure is in the manual. I had that same adjustment in my previous Rancher with push button shifting. Believe me, you will love the P5, its a great machine, its a Honda. How many of those old 3 wheeler are still running around and parts are not an issue for those old machines. Chet