You're not working the purl and knit in the same stitch.
With charts, you read the right-side rows from right to left, and the wrong-side rows from left to right.
The back of the blanket will be the wrong side. So when you're working with the right-side facing you, you want keep the yarn in the back when you're slipping stitches. If you need to slip stitches with the wrong-side facing you, you want to keep the yarn in front. Once you get started, it'll become second nature to keep the yarn on the correct side.
When a chart says to 'purl on the right side and knit on the wrong side', it's telling you that when the right side of the blanket is facing you, you purl that particular stitch; when the wrong side is facing you, you knit that stitch. This, too, will become more obvious as you go along.