It's designed to fit the needles so you can have it handy.
I advance mine for the next row. That way I know if it's on evens I know I'm purling. When it's on odds I'm knitting.
It really doesn't matter how you do it as long as you do it the same all the time.
When mine reads 62 I may only have 61 rows done, but as long as I do it the same both sides have the same amount of rows. If I have to purl 4 rows I purl 4 rows and the counter then sits on 5 waiting for the next row.
If you ever use DPNs or circulars you can also run your cast on tail through the center of the counter so it's hanging off the object (because sliding it on the needles doesn't work for DPNs and circulars).