I bought one in the last couple of weeks, very similar to the one in the link, from costco.
Not using it over the hot tub, I have a retractable awning that covers the hot tub. Using it on my deck.
Sunbrella fabric, cantilevered arm.
The base was different, 500 bucks and 9 ft if I remember correctly. Would easily cover my hot tub if I had room for the base.
I do let it down when I am not using it. Something that large acts essentially as a sail, and cannot readily handle strong gusts. I think you are going to have to have ballast, or custom make a base that will fit under the tub.
Your frame would have to be pretty strong for any side mount to work well. The side mount pictured on the website should work if the frame of your hot tub was strong.
Or so it seems to me, anyhow.
I don't think my original frame was strong enough for that to work well. However, mine is about 14 years old, and was not a well known name.