Here are the promised pictures. I knit continental, so my yarn is on my left index finger.
This is the sample piece i knit:
I show the whole process from WS because that's how you "pick up and purl" in the pattern.
That's the regular "pick up and knit". You insert the needle from the front, pick up the yarn from the back and return to the front:
This is the way you insert the needle with "pick up and purl" (in my humble understanding):
Then you take the yarn like in purling:
And return the needle with the yarn to the back:
In this way, when you have the WS facing you, the edges of the squares will still be on the WS. HTH