If you look online for tutorials involving sticky stabilizer, you are told to cut your length of the stabilizer and then put it, paper back and all, into the outside hoop. You are then told to score an area and pull off the paper to expose an area that you can adhere your fabric to.
I dislike this method because ultimately the hoop loses tension on the stabilizer (the paper is slippery!), and the fabric being embroidered can, and usually does, start to pucker and shift, especially when doing the complicated overs and unders of a Celtic knot. I hate puckering and will do all I can to avoid it. I have yet to have a perfect embroidery sample, but I am working on it.
I will illustrate what I do using one of my large hoops for my commercial machine, but the same idea can be used on home embroidery machines.

As you can see above, having come off of a roll, the stabilizer is curled. To get started, I lay the inner hoop ring right side up on the paper side of the sticky back to flatten the curl as shown below.

Then, I begin to pull the paper backing off the piece of sticky stabilizer.

With the hoop still weighing the stabilizer down, I pull the paper off one end.

Then I move the hoop end onto the exposed sticky stabilizer.

I rub the stabilizer onto the bottom and a bit of the side of the hoop. Then, holding the hoop, I pull the rest of the paper off so that the hoop “catches” the stabilizer.

Attaching the stabilizer evenly around the hoop can take some patience.
This next pic shows the sticky back attached tightly…when I thwack it with my finger it sounds like a drum.

Next, I cut a piece of tear away stabilizer…

…and then hoop the whole shebang.

(Since I now mainly use a rectangular border frame which means there is nothing to hold the tearaway in place, I just wait until I am ready to stitch to slide the tearaway under the hoop. The basting box or placement lines or even just the first stitches of a design catch the tearaway and hold it in place. And since the sticky back does cause a buildup on the needle that causes more thread breaks, I have taken to adding a piece of waxed paper from the baking section in between the sticky back and the tear away. This keeps the needle lubricated so that I have very little build up and very few breaks.)
You will notice when stitching out designs using the sticky back stabilizer that I have added a basting box around the design. In the pic below, you can see the faint line of the basting box.













Do you leave the sticky backing on the velvet? Do you try to peel off the sticky backing off? Do you use this method for the bodice? When I tried this method it sewed great but pulled the fusible tricot off the velvet bodice
I do not have the problem with loosening the fusible interfacing because I also fuse Decorbond to the back of the interfaced fabric before embroidering to further support the stitches. The sticky does come off of the Decorbond fairly easily, but I really do not worry about it that much since I loosen all of the exposed Decorbond to cut it away so that it does not cause other issues as I continue to work after the embroidering is done. Sometimes loosening the Decorbond can also loosen the fusible interfacing, but since I make sure that fusible is really fused well, I do not run into that much anymore. If it happens, I carefully fuse it back down.
Here is a link to a post with more info: https://taoknitterarts.com/2011/04/21/pursuing-the-perfect-embroidery-stitch-out/