iPhone: The card reader should be used with one phone at a time.
Android: Each card reader can be paired with only one phone at a time. If the user wants to connect the card reader to multiple phones, they would need to power cycle the card reader (or wait for the card reader to timeout and turn off on its own) before connecting it to the next phone in the same sitting. You should not have to disconnect from the previous phone as long as the reader powers off and back on.