Does Purchasing A Game Make that Console Licensed?

So me (and my brother) have a Xbox 360 at both our Mom's house and our Dad's house. For this case i will call them console A (Moms) and console B (Dads). Console A has doesn't read disks (I don't mind this because its 7 years old and hasn't been treated
necessarily well) so we try to download games for it often. I also recently transferred our license to console A to play all of the games we have bought. Me and my brother and I saw the recent sale on bio shock and took the opportunity to purchase all three...
The only problem is we bought them at console B (not knowing how long the sale would last) and brought them to console A through a external hard drive. Now only the account that bought them can play the bio shocks when console A should be the licensed console.
So, basically what i'm asking is can a license transfer be set in motion by a purchase. P.S. all other games purchased can still be played.

Sorry if this question was asked or answered before, I couldn't find any answers about this question.

:)

 

Downloading Xbox 360 games with gold on Xbox one

Hey there Cuddly Buns1,

As ngocphi said previously, if you are on a child account that does restrict you from purchasing Xbox 360 games on an Xbox One console even if they are free Games with Gold titles. You would need to make the purchase on an Xbox 360 console and then install
the game from the
Ready to Install section on the Xbox One.

This page has more information about that error.
Troubleshoot Xbox 360 Marketplace purchasing

 

Your purchase cannot be completed at this time. Please try again.

Greetings , That Issue occurs sometimes If your account region does not match your physical region, the only suggestion is to make a new account that does reflect this information correctly. Sorry for the confusion.

Please try purchasing again from the Console and see if it states something like that.

Regards

 

I also cannot do another license transfer for nearly 3 months.

 

When you purchase content it is tied to the gamertag it was purchased with as well as the console it was purchased on. Making a purchase will not start a license transfer. It just determines what console has the license for that game. If you want the console
license on console A, you will need to wait until you can do another license transfer.

 

ok I assumed when you performed a license transfer it transferred all licences though

 

It transfers all licenses you had at the time that you perform the transfer. When you buy content after performing the transfer, the license for that content will be attached to whatever console you purchase it on.