To me those little blue bits under the raised red row is where the new yarn colour is joined in. Often the colour is worked on the RS row so that these colour bumps are hidden on the WS of the fabric but I think here they used it as a design feature.
To me it looks like a few rows of garter stitch.
@Shintoga the method you describe sounds a little like what happens when weaving in the ends whilst knitting, a kind of up down with the tail or contrasting colour to catch it across the WS but in this case the RS.
@kaylo maybe you could try out the couple of suggestions here on a swatch and see what works?
I’m impressed initialled stockings are on the go, I’m still on summer tops!