Thanks for the question. The following article provides more information:
When you turn on iTunes Match or Automatic Downloads, or when you download past purchases on an iOS device or computer, that device or computer becomes associated with your Apple ID. This article describes how to manage these associations.
Your Apple ID can have up to 10 devices and computers (combined) associated with it. Each computer must also be authorized using the same Apple ID. Once a device or computer is associated with your Apple ID, you cannot associate that device or computer with another Apple ID for 90 days. You can view which devices or computers are currently associated, remove unused devices or computers, and see how long before they can be associated with a different Apple ID from the Account Information page in iTunes on your computer.
It may be that your iPhone is not available to associate with the secondary account, as it is still within the 90 day limit. To be sure, attempt to download a previous purchase or sign out and back in to iTunes & App Stores in Settings.