USBHost_t36 definitely supports hubs.
It is very close to "transparent", but you do need to place a USBHub object in your code for each hub chip you want the library to be able to support. From the photo, that Adafruit product has 1 hub chip. Many 7 or 10 port hubs are actually 2 or 3 chips inside. For example, most a 10 port hub is typically three 4 port hubs, where 2 of them are permanently connected to 2 of the first 4-port hub's ports. So if you don't know what type of hub a user will plug in, best to put 3 or 4 extra USBHub instances in your code, in case they use a hub with several chips inside. Most of the library's examples of 2 or 3 instances, so just copy those lines & edit the instance names.
Assuming you have enough hub instance, the library manages hubs & devices connecting and disconnecting from them automatically.
If you do find any hub that doesn't work with the library, please start a thread to report it. This Adafruit one is easy. If it's a no-name hub, try to figure out where you bought it. Fixing USB host issues is pretty much impossible when we can't buy the problematic device.
On hubs, I can tell you the 5 I have here work perfectly. Many people have used other hubs too, so no bugs are currently known about any hubs.
FWIW, almost 1 year ago we did have a report of a specific USB 2-port hub that didn't work. It was a bug in the library, which was fixed last summer. It turned out the bug wasn't actually in the hub driver, but a rather subtle bug in configuring virtual USB pipes deep within the library. I wrote a detailed blog article about the bug hunt.
https://www.pjrc.com/usb-hub-bug-hunting-lessons-learned/
Something the library does not do, is check the USB power descriptors. If you plug a power hungry device into an unpowered hub, or if you try to chain unpowered hubs, the library will not notice and will try to use them anyway. The USB spec says hosts are support to read the mA spec from each device and know whether a hub is powered (like a wall wart) or unpowered (getting its power only over a USB cable) and detect when you try use too much power, and refuse to enumerate the new device. USBHost_t36 does not do any of this checking. It will try to make use of whatever you plug in.
For best compatibility, you'll want to make sure you give that Adafruit hub power on its JST connector.