I contacted the paper to run my ad on a Monday. The ad ran on Friday of that week. I had my affidavit from the paper in the mail three days later, the following Monday. So, in my case, I received the affidavit well before the ten days. Regardless, I waited ten days after the ad before I filed my application at the Prothonotary's office.
I imagine the ten day requirement is intended to give those who read the ads in the paper enough time to write a letter and send it to Superior Court / Office of the Prothonotary in the event they see you ad and have reason to suggest you should be denied.