Once you dd the image they provide, you'll notice that you can only boot from eMMC when the SD is not inserted and if you inser it after boot, the system doesn't even discover the devices.
There is an easy fix for this.
At boot, uBoot looks for /boot/bananapi/bpi-m3/linux/uEnv.txt
and loads /boot/bananapi/bpi-m3/linux/script.bin
that contains additional configuration, like how to manage the SD, in binary format.
You just need to follow a few simple steps to enable SD discovery after boot (there is a way to boot from the boot partition on the SD and then load the OS from eMMC but I didn't have time to experiment with that).