Believe it or not, BOTH are correct. Technically speaking, the person at Lowes is correct. Any inside corners should be caulked. However, so long as your shower floor is tile, it's not attached to the structure in any way. It's "floating" inside a membrane, which means it'll move WITH the walls instead of against them, and a movement joint really shouldn't be needed there, so your installer is correct, too. However, I disagree with him that the corners of the shower should be grouted. Those do need to be caulked.

I think you are supposed to put caulk wherever there is a change in planes or materials. So, like, where two walls meet, where the tile on a horizontal surface (your floor) abuts a vertical surface (the front of your tub), and where there is a change in materials (like from tile to tub, even if those two surfaces are both horizontal or both vertical). But this is just what I've read. You probably want to get somebody real (that's actually done tile stuff) to weigh in here.

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:

If it's a preformed unit, it should be fine to grout all the corners. If it's built in place, the inside corners should all be caulked, and yes, all return tiles should be flush to provide a smooth transition.