You’re confusing this Octagon swirl pattern with the other one. The Octagon says to use a set of size 5 dpns with 5 needles, you CO 8 stitches not 6, so you would still put 2 sts on the 4 working needles. If you’re using magic loop you ignore that part though. CO all your stitches, pull the cord out between them so you have 4 sts on each part of the cord (or 3 sts if you use the one where you CO 6 stitches). Then you take one of the tips in your right hand to join the sts and work the first round.
One thing that might help you is to check out tutorials or patterns for top down hats. It’s the same principle, knitting in the round. With those hats you keep increasing, which you’d have to do with the coasters, and it comes out lying flat. When you stop increasing and knit straight, the sides come in and it’s the straight down sides of the hat. If following hat directions, you would stop when it gets to the size you want. I would suggest pulling the tail on the first round or two to close the hole.
Have you tried crochet for the coasters? In making a hat in crochet, you crochet in a circle. You keep increasing. It looks like a flat plate. You stop increasing at a certain point to make the hat curve inward and downward. I think crochet would be better for something like this.