I'm asuming your stitch before the YO, P1 is a knit stitch, right?
I think I wrap my YOs differently than most people, but when I do it, I bring the yarn under the right needle tip, then over the top. In that case, I would then continue by bring the yarn back under the needle and to the front for the purl.
You probably YO in normally prescribed way, but, well, bringing the yarn over the needle. In this case, you are simply laying the yarn across the top of the needle and leaving the yarn in front for the purl. The key is that you do not want to create 2 wraps, which you'd have to do if you brought the yarn back as though to knit. This means that you appear to be doing half a YO. That's OK, as long as you are creating a new loop across the top of the needle, you are fine.