yeah, your understanding is pretty much correct accept the cartridge status is stored in the chip and not the printer.
Every time there is an operation on the printer that uses ink, the printer sends a specific voltage to the chip to lower the chip’s ink level. When the ink level becomes low enough to warrant a cartridge replacement, the printer pauses in mid-print and sends a kill command to the chip (this will normally make an Epson OEM chip not able to be printed with later). This kill command does not kill the IJM ARC chips but simply resets the chip. In oder for that reset to be activated though the printer needs to see that the cartridge was taken out (loss of connection) so you take the cart out, fill it, and put it back in and the cartridge reads full again.