I do not think that an e-Recovery would ever contain “Continue with MiAssistant”. I think you are probably seeing an Xiaomi / Android recovery. This is what e-Recovery looks like
On many devices there is a bit of a trick to your first boot into e-Recovery. Having flashed your new recovery, if you have the phone perform a “normal” shutdown and reboot cycle then your new recovery will be overwritten and you have to flash it again and try to boot into it without a normal shutdown cycle. I don’t know this phone so cannot tell you the exact button presses, but here is a description for Samsung First boot into Recovery.