Hi @Anonymous,
I'm probably butchering this explanation, and sorry for repeating myself if this is not the answer you were looking for. The way Fusion entitlements work (and for right now let's pretend you bought only one), in a nutshell, is when you buy a commercial license of Fusion, it is tied to one email address on your Autodesk Account. That email address can be used to log you into Fusion on any computer that has Fusion 360 installed. Using that download link (or by using the Free Trial download link here), you can put Fusion 360 for free on any computer you want. The limitation is here you are limited to the trial, or the computer will stop working UNTIL you sign in with your Autodesk email. This is where it notices if you have a valid Fusion entitlement. So theoretically you can use Fusion 360 on your home computer lets say by just installing the software and then when prompted log in (just like with Facebook for instance). Then once you log in, you will see all of your cloud data. Now, let's say you go to your workshop and open Fusion on that computer. Same workflow, log in using your Autodesk email (same one that you used on your home computer), and you will see all of your cloud data again.
Since you've bought 2 licenses of Fusion 360, your Autodesk account is now the Contract Manager and you have access to 2 licenses. The first license is automatically assigned to your Autodesk Account (which by the sounds of it is what you want). By following the workflow in that link, on your user management page hit the blue add user button (looks like a plus sign). You can assign a user to that empty license by entering their email address and name when prompted. Once you hit save, it will bring up a page that will allow you to assign any available licenses. Once he is assigned that license, that email address is now valid to use Fusion 360. You can verify this by logging out of Fusion 360 (if you are automatically signed into your main account) and then logging in with the secondary email. Then, go into the Help menui (top-right corner of Fusion 360) and select About. Under Active Plan you should see it say Subscription or something along those lines.
To install Fusion 360 on your new computer, I would just use the link I provided above for the Free Trial. Like I said, once you log in using your email, it will recognize whether or not you have paid for a subscription using that email address or if it is indeed a trial.
Thanks,
James Youmatz
Product Insights Specialist for Fusion 360, Simulation, Generative Design