We track two types of conversions: Click through conversions and View through conversions. In cases where you've paused a campaign but you receive a notification about a conversion occurring, there are two reasons for this:
1. If it is a View Through Conversion (VTC), that is a user who was served your ad while the campaign was running, did not click it, but later came back on their own and converted after the campaign was paused.
2. If it is a Click Through Conversion (CTC), the user clicked the ad while the campaign was running, but did not convert at that time. They later returned to the site on their own and converted after the campaign was paused.
You can learn more about that here.
If you look under Manage-> Conversions, you'll be able to see what type of conversion this was, and when the click/view occurred. By default, we track conversions in 30 day conversion lookback windows.