Note that all the pics on that amazon listing show the kit upside down.

When you install it the wider brace goes on top, and the gear cluster on the right.
Hubs for these axles usually use some form of D or double-D hole as the axles usually have flatted axles to match. This one looks like it may use two different axle / hub types, with the driven side (right wheel) being a different diameter on the inboard side where the D or double D hole is, and the outboard side being the same small hole size as the non-driven side (left wheel)
On this kind of conversion axle, AFAICT the left wheel just rolls along on whatever axle bearings it has, and has no braking or drive on that side. All the braking (via the band brake on the axle) and drive are on the right wheel. (hopefully the bike already has a good front brake)
To use disc brakes on the hubs (if you make or find some that have rotor mounts), you'll have to build caliper mounts to bolt to the fender-frame mounts.
Do you have any fabrication skills? If so, you can usually make your own hubs easily enough, or even just modify existing ones that are what you want but too narrow. (if they are steel, you can just cut them in the middle of the tube, then cut a length of new tube of the right length to make the hub the width you want, whose ID is the same as the hub's tube OD, slip them together, and weld or braze them together (just make sure you line up the spoke holes in the flanges the same as they were before).
(it's possible that a good epoxy, coating the OD of the hub tube and the ID of the new tube, before slipping them together, might even be enough to secure them, if all the loading is handled by the flanges to the axle and the tube just connects them).
BTW, whatever it's speed was as a bike, as a trike, it could be a good idea to limit it's speed to around 15mph or even 10mph or less--in my experience with the geometry you can end up with on this kind of conversion, it is likely to tip over and crash at the slightest twitch of the handlebars before you can even react at higher speeds than 15mph, and is likely to be unstable and hard to control above 10. Sometimes even 10mph is too fast.
Hopefully yours won't have this issue; since there's no info on what bike is being converted, there's always a chance it could turn out better.
The lower the COG is, the better, and the more weight is on the outboard points of the rear (at the wheels) the better, but both of those are hard to do with that style of trike kit and when converting a bike into a trike.
Another issue is the steering; trail / caster on a bike is different than what's needed on a trike, and sometimes the one just doesn't work like you need it to on the other. It's possible to change this by changing the fork, or sometimes other methods, to improve handling if necessary.
Any suggestions? I'm thinking about building trikes for me and my wife, too, so I'd like to get good at it.
If you're going to build trikes, I recommend taking a look at my SB Cruiser thread. It performs and handles well up to the 20MPH speed limit we have here, and if you were building one from scratch you could make a few improvements to the design that I've never gotten around to on mine because I use it every day and would have to take it out of service to do (like rear disc brakes).
There are a series of versions of it that have different looks and usefulness for different kinds of operation.
There are many other kinds of trikes, too, depending on your needs, usage, and skills.