From the web page, the AXE I/O Bundle includes AmpliTube 5 MAX ("AT5 MAX"), AmpliTube 5 SE (that one seems redundant to me), AmpliTube 4 Deluxe and 10 T-RackS 5 processors,
Those T-Racks processors would run in the free T-RackS 5 Custom Shop ("TR5 CS"). The CS edition of the software is free; any bundled TR5 processors will run in that software. The TR5 SE, TR5, TR5 Deluxe and TR5 MAX products include different numbers of processors. Which processors you can use depends on the Serial numbers you have; you can always Try (and buy) more.
The IKPM (the Product Manager) is a relatively new product, designed to carry out downloads, installed and registrations. But it does not support all products:
The IK Product Manager gives you one central destination to register any IK product, hardware or software.
If you register hardware that includes bonus software content, as soon as you’ve registered a pop-up will inform you of the software added to your account and they’ll be right there in the software tab.
and
The IK Product Manager is designed to support all current product versions; therefore, all the legacy products are not supported and will continue to be handled by the previous Authorization Manager.
Can you tell us which products that you have received Serial numbers for?
Not the actual numbers, of course, but for which products?
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I think that you should be able to Register the AXE I/O hardware through the IKPM (indeed, there is a screenshot on the IKPM web page showing AXE I/O) then see the pop-up about the bonus software added.
You should then be able to download / install / authorize AmpliTube 5 MAX and and T-Racks 5 CS through the IKPM. Click the [Products] tab under each main product name to see them (at least, that's how I see them here).
If the installers did not do it, do the same in the IKPM for the new Custom Shop program (currently v2.0.0). Run that program, log in, click your Account Name and select "Restore my Purchases".
Phew!. Now you should be able to run the standalone AT5 or TR5 program and configure their I/O settings. Then access of the gear models (loads in AT5 MAX and those 10 processors in TR5).
I may have missed something as I have not needed to do this, but let us know how it goes.