My picked up stitches are always too loose. After I’ve worked a row or more, depending on what I’m doing it may need a lot more rows, I go back to the last picked up stitch and start working out the excess yarn one stitch at a time by pulling on the legs on the knit side all the way to the beginning. I came across a handy trick that helps with this: hold contrasting crochet thread or something else thin and smooth with the working yarn when you pick up your stitches. When you work into them, treat yarn and thread as one. You can then follow the thread to easily find the legs of the stitches to adjust your tension.
Since you’re working on the RS with the yarn at the back to pick up stitches it makes sense that it’s on the inside. I don’t think you’re doing anything wrong. You’ll just move it to the other side of your work if you need to.
What cast on are you asking about? I don’t use a slip knot with a long tail cast on. Here’s one way. https://www.youtube.com/watch?v=aiRfeGGRmvA