You need to have the same account attached to the device where you want to install the application as well. I purchased an application on the Android store and then I was able to install that application on 10-15 devices, after I added my account. If you want to install it normally under a different account, then yes, you will have to buy it again through the Play Store. Go to Settings > Accounts > Google. Add the account, then search that application and it should be free to install.