Adding chemicals seems simple on the surface. Measure, add to the water, and mix.
That said, there's some important details to follow, and I wanted to understand the reason behind the recommendations.
Here's some more context around the direction label that I wish was more easily available:
Why add chemicals to the filter compartment?
First, this is where the most concentrated flow of water is within your hot tub. This will help mix up the chemicals and ensure they are easily distributed. Second, adding granular chemicals to the main body of water can actually damage your hot tub. If they are to land on the bottom/seats of your hot tub, they may cause discoloration, take longer to mix up, and potentially are harmful to occupants if they haven't fully mixed and come into contact with skin.
Pro tip - Try to drop any granules on your filters. That way discoloration/damange happens to replaceable components. In a worse case though, discoloration from chemicals happens in an area that is not regularly seen.
Turn off aerators!
I learned this from experience as it wasn't always on the directions of chemicals. When aerators run on your hot tub (the little knobs that increase jet pressure by adding air), it actually causes a reaction that increases pH. So while mixing your water, make sure they are all off so you aren't raising your pH (especially if you are trying to lower it)
How Long to Mix Water
The Hot Spring manual makes it sound very simple. Press the clean button (which runs 1 set of jets for 10 minutes), add chemicals, leave cover open, and close when done. That said, I've noticed the labels of chemicals call for different run times. Always circulate the water for the time listed on the label (SpaGuard pH decreased lists 30 minutes, SpaGuard Phosphate Reducer lists 2 hours).
Use All Jets Systems
If you follow Hot Springs recommendation and use the clean function to mix your chemicals, you actually leave water within one jet system. Every time I mix chemicals, I use the primary jet system to mix, then run the secondary system for a minute or two after to ensure that water moves as well.
Leave Cover Off
I would recommend leaving the cover off for at least 30 minutes after a chemical application to be safe. Covers aren't cheap. If you are shocking the hot tub with chlorine, make sure to leave it off for a few hours to give the chlorine a chance to gas off. After shocking I also will open the hot tub from time to time over the following 24 hours just to help make sure none is trapped.