Ads are rarely downloaded in the background. They usually load when the app is started.
Instead of guessing, there's an easy way to actually find out what used up that data.
Most of all, you can easily verify all data usage on your phone. You can check a breakdown of data usage by app in your phone's settings. Android "Mobile data usage" in the settings is more accurate in this regard, as it displays a breakdown of all mobile data usage by app, including the data used by the system's components themselves, so it should be easy to pinpoint the culprit. The total usage adds up to similar amounts as displayed in your PM self-serve. On iOS you can check data usage by apps in settings too, to see if any of the installed ones went rogue, as well as the total data usage as well, which should add up to the amount Public Mobile charged you for.
The location of those options depend on the device you are using, but you will find those options by going into settings and searching for "Mobile data usage" on Android and under "Settings > Cellular or Settings > Mobile Data" on iOS.
Since you will see a detailed breakdown, you will see what exactly used up that data and act accordingly by changing settings on that app, disabling background data transfer or uninstalling it altogether in case it's a rogue app.
