All updates to OnSong are free so unless there is an issue with your Apple ID, you will not be charged. If you are currently running a version of OnSong older than OnSong 1.92 from 2011, you may need to purchase/acquire OnSong again as the app was relaunched in 2012. You can check your version of OnSong by going into the Utilities Menu by tapping on the gear icon in the Menubar and choosing Settings. Select the About section and view the version of OnSong on the right. You can review OnSong's release notes to find if you need to update.
If you are being asked to pay, it could be caused if you are not signed into your device or the App Store with the Apple ID used to originally purchase OnSong. You may want to check your purchase history under the Apple ID that you are using to ensure that you've purchased OnSong in the past under that account or contact Apple Support for assistance.
If you were charged again for the app, please contact Apple as developers do not have the ability to review any information such as your purchase history or billing information. Developers cannot issue refunds since the purchase is made directly with Apple.