Good description of a basic process.
Minor quibbles:
Video shows the foam being left flat when upholstering; the foam should wrap up when you do this. Worst part of the video is when they cut the star into the vinyl and then fold bits up to staple, but leave the foam ring flat.
Also, the video doesn't say enough about stretching when upholstering - this is an ART. If you don't stretch, your fabric will move and bunch up in play. If you stretch too much, it pulls out from your staples or tacks. If you stretch unevenly, your weave/pattern is distorted. And the right tension for the felt is not the same tension as for your rail, and both are material-dependent. There's a lot of room here for good or bad craftsmanship!
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Caveat: I played the video with no audio, so maybe this is all covered...