The counter for rares resets when you get a rare by drawing them as a lucky roll. The same for superrares that owns a separate counter.

Lets say you got mei at your 60th draw in kage and then you use another 30 scrolls and get onoki, at this point the counter resets and you don't get a rare for sure at your 120th draw, but at your 150th. I hope this clarifies a bit.