Knit or Purl? Confusing Lace Grid

So I’m working on a pattern called Comfy Hooded Scarf (designed by Jodi Snyder; it was off of and I’m rather confused about the lace grid on the back.
I’ve attached a picture of the grid.
In the key below, it notes that on the right side, the white box means knit, while on the wrong side it means purl, which is clear enough. However, would that apply to the other boxes about the ssk and k2tog, etc. Should those become their purl counterpart when on the wrong side? I looked at a picture of the finished product and it looks like there is just stockinette under the lace triangles. Can anyone clarify?

It looks like the ssk and k2tog only occur on the right side rows (the odd rows) from this chart. If you do come to a place where the decreases fall on a purl row though, yes, do the purl version of the decrease.

Ooooh, I can’t believe I did not see that the decreases are only on the right side. Thank you!