Hint 1: Sometimes it might be necessary to clear the Play Store (or the other app store) cache/data. You can do it → Android OS Settings → Apps/Application Manager → All → Google Play Store → Clear Cache/Data and then - if necessary - remember to log in again with the right account.
Hint 2: Make sure you activate the license of the correct app: if you bought the license in-app, all you need to do is to download the free app (purple icon with BC/30) and the pro will be automatically unlocked within that app. In some countries, there is also a separate pro app (red icon with BC/30), which is the solution for those users who couldn't use the IAP system. If you have this license, you download the pro app directly.
Please remember, that the license is bound to the account and the app store and it is therefore not possible to transfer it either to the other email or to a different store. Please note as well, that we - as app developers - are not responsible for the download, purchase and license activation processes in the different app stores. We just upload our apps there.