Yep...any "change of plane" oughta be caulked. Horizontal OR vertical. When you caulk your tub, I recommend that you fill it about 3/4 or so....THEN caulk it and let the caulk cure before draining it. In that way, when in use, the caulk doesn't "stretch" too much and seems to last longer.

Update on my dilemma, I filled the gap with clear silicon and covered with a strip. I didn't notice until I opened the strip that it was almond color, not white. For the corners I cut the strip in the middle fold and it adhered pretty good in the corners. It will do for now. We plan on converting to a shower with no tub sometime before the end of the year so that's okay.

I am a DIY'er and did a pretty significant bathroom remodel where I did all the tile work. On my shower, I used Laticrete Hydroban and durock for my walls. At all corners and at the tub flange, I used fiberglass tape embedded in thinset, sort of like your video. Much cheaper I imagine. The Schluter Band is water and vapor proof I believe. You will be using Redgard to achieve the same water management goal, so I don't believe you would need the Schluter product. All changes of material and planes will be covered with the fiberglass tape and thinset. All the fasteners will be covered with thinset. All valves are set with tape and thinset, or the product included with the valves. My valves came with a taping product that I thinset into place. Then everything is coated in the water management membrane such as Redgard or Laticrete. I filled in all small voids with thinset. I don't have a picture of the bottom of my shower pan and Durock, but I think I taped it with the fiberglass tape. It has been some time since I did this job. Below, is my thinset and taped cement board. True Confessions, I don't think I have enough fasteners, nor the right kind, in my wall, and I worry about this flaw in my shower. I had drywallers hang this for me when they did the rest of the room. I assumed they used the correct fasteners, but they didn't. They started out with galvanized nails, which I believe would have been ok, but I wanted screws, so they switched to the drywall screws. I had the Durock screws, but didn't give them to the workers, assuming they had their own. They didn't. So after they left and I saw the, I tried adding my Durock screws into the wall. I couldn't do it, I just wasn't strong enough. DH was out farming and wasn't available to drive more in for me. So I proceeded. My mistake, as I learned later the drywall screws deteriorate in cement board over time because of the alkaline conditions. I confessed to DH that the walls might fall down in a few years. He said, "well when they do, we'll just fix it." What a relief I felt, I no longer carried this burden of knowing that I flubbed up: Here is the bottom where the coating is onto the shower pan. It hard to see, but the pan and walls are totally sealed in the Hydroban. Click it open to see the bottom of the walls at the shower pan, where I taped a plastic sheeting to protect the pan. Be sure to follow the recommendations for thickness with your Redgard. This is Laticrete Hydroban: If you click the picture open you might be able to see the valves sealed with the Hydroban. This green tape is by 3M and is very strong used for taping concrete I believe. It was great to use to hold hanging tiles into place until the thinset cured. You will want this tape for your tiling job, I loved it:

The new puppy chewed up the camera. Sounds like you did a nice job.