Firstly, it’s definitely necessary for one person to tap in and out with the same “thing” to be charged correctly. Your phone is a “thing” and your card is a different “thing”.
As a result, as far as I know, you should be able to use one of those “things” each to make two separate, simultaneous and complete journeys at the same time. I’ve not tried it but that’s how I understand the system to work.
As far as appearing on a TfL online account, my card simply appeared twice. Once for the card itself and once for the Apple Pay version of the card. (I renamed one of them to make it clear which was which.) As stated above, they’re treated as two two different cards so will each be charged and capped separately even though they end up debiting the same bank account.
