What am I doing wrong with the AndroidPit app service?

I have just joined AndroidPit and purchased an app through the site. I followed the instructions to install the AndroidPit app onto both of my devices (a Samsung Nexus S smartphone and an Asus Transformer Prime, both running Android 4.1). Third-party installation is set to allowed and my account has been validated, but I cannot get the app I bought, through the AndroidPit app. On both of my devices, I get the "you must install the AndroidPit app" dialogue, even though it is on the app. edit: I have tried to include a picture of what I mean, but being a new user I am disallowed from doing that

I have double-checked and made sure that third-party installation is set to allowed on both devices. I have double-checked and made sure that my AndroidPit account is activated. I have double-checked and made sure that the app that I paid for is acknowledged as paid for. I have rebooted both of my devices. I have refreshed the AndroidPit app on both devices, but still, when I press the My Apps button, I see the dialogue as pictured above. What am I doing wrong? I would like to get the app that I paid for. This is very frustrating.