Why do our iPhones keep asking for passwords of other users? Our client's employees all have iPhone 6s. They don't share phones, and have never used each others, but strangely, as one user tries to download an app at the App store, it then asks for a completely different persons' iCloud password. The only thing these phones share is a WiFi network, and mail accounts on an Exchange server.

This has happened to two other phones within the same client employees. One of the phones actually asked for a completely different client iCloud password, even though these two people have never met before.

Why does this keep happening?

Update: I have answered this myself, and marked as the correct answer because that is exactly what were happening.
Is this an enterprise setup? How are the phones being managed? MaaS360, OS X Server, ect? 

It sounds like the users are connected to the same App Store ID and all have different iCloud accounts they are logged into (or vice versa).