The needles are tools. People who write patterns try to be explicit but one way of knitting in the round makes the same product as any other. If you prefer knitting round by using dpns, use them.
Many patterns, especially older ones say to start on circs, and switch to dpns when the diameter gets smaller than some limit. This is partly because materials weren't as good, and the circs were too stiff to easily do a magic loop. The DPNs may not have been easy to acquire in different lengths (I'm guessing; I'm not THAT old). It really doesn't matter. Watch for "ladders" or loose stitches at the edge of whichever one you use
I'd read that pattern, from what you write, that you'd be switching to the same diameter of needle.
oh, thank you, thank you, thank you for the advice!!!