iOS
AT Internet's app tagging is done within the app and therefore does not directly measure anything external to the app.
Unfortunately, it is not possible to know the origin of downloads on iOS, since Apple does not provide the information of the origin of the traffic (referrer) to the application from the download page.
If you want to know the number of downloads of your application on the Appstore, it will be necessary to rely on the figures directly provided by Apple.
Android
Concerning Android, and as explained in the dedicated documentation (https://developers.atinternet-solutions.com/as2-tagging-en/android-en/campaigns-android-en/marketing-campaigns-android-en-2-3-0/), it is possible to know the number of downloads following a marketing campaign, since the Play Store allows the conservation of the referrer.
It is customary to place in the Play Store referrer the link of the page preceding the arrival on the latter in order to follow the origin of the download through a marketing campaign, which will appear in your analyses as soon as the application is launched.
For instance: https://play.google.com/store/apps/details?id=com.atinternet.android&hl=fr&referrer=http://wwwmonsite.com/mapage?xtor=AD-123