The thing is that's an extremely low res cell phone video. Cell phone cameras are bad enough but cell phone videos certainly aren't going to show what's left behind after those two polishing steps.
The video is showing using a cutting pad to hand apply a compound. Ultimate Compound is not a pure SMAT polish, it will initially leave behind marring that the Ultimate Polish likely won't remove by hand. The Ultimate Polish will reduce it for sure, but on a black car in real life unless you can remove all the left over marring from Ultimate Compound, Ultimate Polish which by hand with a finishing pad would take a really long time, you'll have reduced the finish quality especially considering the OP's car is brand new.
It's an improvement sure in the video but that's from basically a severely damaged car as is. Almost anything would be an improvement. And the amount of material Ultimate Compound removes by hand is entirely unnecessary in the OP's situation.
The OP's situation is a brand new car, you shouldn't be compounding a new car to begin with. You'll still get better results and less material removal using a finishing polish to remove buffer trails than using a compound and polish by hand. Not to mention buying those 4" pads, and holder plus Ultimate Compound AND Ultimate Polish will cost more than the 6" buffer and a wool bonnet, microfiber bonnet, and Ultimate Polish. You can forgo the holder but try to use a thin foam applicator with rubbing compound and you'll be either working for a really long time, or like most people increase the pressure to get the work done faster at the cost of marring the paint and uneven correction.
So if you've got a buffer, you're better off just using the buffer and Ultimate Polish instead of Ultimate Compound and Ultimate Polish.
Believe me years ago I tried doing mobile detailing by hand, it's no picnic and the results are always less than satisfactory if you're expecting any decent correction.