TL;DR: Beeper doesn't fully support this feature yet. 

How does Android Dual SIM on Beeper behave?

For sending messages, Beeper will respect the phone number you have set as the default on your phone settings. Beeper will manage all chats imported with the secondary phone number and any messages received by the secondary number while keeping the secondary phone number's identity intact.

Q: We don't currently support Dual SIM on Android. Will Beeper always use the default number on Android Settings?

A: Yes, right now, it will use the default number if you start a new chat, but it also uses the number on which you received the message if the chat already exists. So, if their default is ABC and they receive a new chat to XYZ, the reply will go from XYZ.

Note: If you want to create a new chat with the secondary phone number, you can start it using the native Google Message app, and it will be in Beeper within seconds. Onward messages will be sent/received from/to the secondary phone number.