There are 3 software "things" on the 64drive.
There's the FPGA configuration, which makes the thing work, there's an included bootloader, which is booted by the N64 so that it can take control and poke the SD card, and then the menu inside the card which gives you the ROM list and the rest of the user functionality.
When you turn the power on, the FPGA is "empty", so the first thing it does is try to load a configuration binary to work with from a flash chip on the 64drive PCB. When you turn the power off, that configuration is lost and must be loaded again next time power is turned on. Resetting the N64 doesn't power-cycle the cartridge, so the FPGA still has the same config file (or firmware) as before the reset. Updating firmware only erases the flash chip and writes the new firmware binary. It doesn't and probably can't force a re-load. You need to cut and restore power to the FPGA for that.