Picking up stitches at the end of a round?

My first project on DPNs was a pair of fingerless mitts. When it came time to work the thumb, these were the pattern instructions:

Using smaller needles work k1, p1 rib across the stitches you put on a holder, beginning with a purl stitch
Then pick up 3sts at the top of the thumb (where you cast on 1 st after finishing the thumb gusset).
Place a marker for the beginning of the round.

Most of the instructions I’ve seen here are for either picking up stitches along an edge or at the beginning of a row or a round with a new length of yarn. How do you pick up stitches at the end of a round?

What I did was leave a longer tail when I started the round, and when I got to the 3 stitches I needed to pick up, I used that tail to do so. After the stitches were picked up, I had to do some moving of stitches from one DPN to the other, and it was confusing. Since the mitts were for my own use, I didn’t really care if they were “correct” or not, but I’d like to know the right way to do this if I come across it again.

When you finish the K1P1 stitches, leading up to the spot where you’re supposed to pick up stitches, the last stitch that you work will then be the first stitch on the needle in your right hand and it will have the working yarn (the yarn from the ball, not the tail end) attached to it. Use the working yarn and the tip of the right needle for picking up the 3 stitches at the top of the thumb. Place a marker after the 3 stitches are picked up and that will be the new start of the round. Your working yarn will be ready to go for knitting the thumb.

When I’m working on DPNs, I end up knitting inside out, so do I run the working yarn across the exterior of my tube (the actual mitt interior) and pick it up through the inside of the tube (the true exterior of the mitt)?