Downloaded ios app never shows as purchased
Are you using the same Apple ID for iTunes on all of these devices?

Check your iPhone settings > click on [your name] > click on iTunes and AppStores > then where is says your email address at the top and make sure that the emails match.

If they do, leave a comment stating that they match. What's going on is that if they do match, then check for items that you have purchased to see if they are are there. If they aren't you need to call Apple Support to speak to iTunes Support. 

But MAKE SURE THAT THE EMAIL IS THE EXACT SAME EMAIL ADDRESS.