I have had exactly the same problem when I first set up my wife’s account on her phone.
When I added her phone as a presence tag, it replaced mine. I had to remove my phone (now replaced by my wife’s), then uninstall the app on both phones, because the entry on the list was gone on one phone, but tombstoned on the other, with no option of removing it.
After re-installing the app on both phones, I was able to get both of them added to the list by using steps similar to the ones @stevesell posted. I bet, if I had followed these steps from the beginning this would have worked out of the box.
There is definitely some buggy behavior with setting up multiple iPhones as presence tags. Luckily, you likely only have to do it once.
Still would be great to fix this to lower the entry barrier for new users. I so wish SmartThings had a public bug tracker, or at least a way of submitting bugs through a web form of sorts…