The first thing to do is a sanity check. The Beryl has three Ethernet ports, one of them is a dedicated WAN port for connecting to a cable modem and other routers. Do not use that port. Use the WAN port only to connect between the Beryl and the home router. Be sure to use one of the two LAN ports to connect the Beryl to the ASIAIR.
If that is not the problem, the next thing to check is to get really close (like centimeters, not meters away) to the ASIAIR, and connect the iOS device directly to the ASIAIR's hotspot by selecting the hotspot in the iOS WiFi Setup.
Launch ASIAIR and if you succeed in connecting to the ASIAIR WiFi, check the Wired Ethernet item in the ASIAIR Setup window (the one with the WiFi icon). Does it show "Connected?"
If it shows "Not connected," then you are still using WiFi to connect between ASIAIR and the Beryl, and that will never work very well. The whole point in using the Beryl is so that all connections to the ASIAIR is made through the ASIAIR's LAN port, instead of going through the flakey ASIAIR WiFi radio.
If the Wired Ethernet shows "connected," tap on the "connected" text on the right of the menu, and you should see an IP for the ASIAIR in a different window. That should be a recognizable address of your home network. Note this address down.
Now switch the iPad's network back to your home network, and relaunch the iOS ASIAIR app. If ASIAIR app still cannot find the ASIAIR box, tap on the "Connect via IP" text and give it the IP address noted earlier.
Once you have successfully connected, it is advisable to go the router and reconfigure the home router to use that as the fixed address of the ASIAIR. This way, it does not change over time and you can connect via the same IP address in the future. This same address is also the address to access the Samba file server on the ASIAIR to download your images (using macOS Finder>Go>Connect to server... menu).
Chen