For anyone else reading this, we cover this issue all the time and have created many threads about it.
The new AndroidPIT app v2.x cannot install apps for you. It simply replaces the old ''content'' app with a new one. The App Center app - downloaded from the link above - is and always has been the one to use for installing and updating apps bought from AndroidPIT. So you need to have it installed for your purchases and updates to work. We know it's a bit confusing and we apologize for that, but we couldn't update everything at the same time.
However, it is up to app developers to upload new versions of their apps to our servers, so if you aren't getting updates (and you have the App Center app installed) then you need to contact the developers to ask them what's up. Because the app is theirs we can't take updated versions and distribute them to our community unless they give us the permission to do so (by uploading the new versions).