I'll give it a go as a noob. Hopefully I'll get enlightened.
1) Spraying his "Secret Grout Prespray" DIRECTLY onto the caulking and baseboards. I would put solution down with a flat mop avoiding them altogether. I guess the main issue here is that if the seal is poor then solution will wick up into the baseboards from behind the caulking? Also if the baseboards are MDF he's going to ruin them
2) He then proceeds to work the solution INTO the caulking with a grout brush? If I had to clean caulking and baseboards I'd just slightly damp wipe with a mf using only water
3) Aerosol-izing the solution which I assume has some pH around stainless. He should again put it down with a flat mop.
4) Working the solution into the corner next to the stainless with a grout brush. Again he's getting solution on the ss and potentially irretrievably into cracks.
5) I don't know if rinsing/extracting with a carpet wand is bad or not but I would protect the baseboards whilst I'm doing it
6) He's getting slurry on the top carpeted stair.
7) As for the sealer and how it was applied I don't know but he is drying it with a crappy fan...maybe that will cause uneven distribution of sealer?
8) He should protect the carpet from his hoses