I had trouble with that bit of gameplay as well. Let me try to summarize how it works with an example:
1.You talk to one patient.
2.He has a flashback where he meets one of the other patients.
3.You visit that second patient.
4.You use your PDA (don't take it out of the inventory and click it on the patient, just use it in the same way as when you'd phone someone) and play back the recording of what the first patient said while in the room. The patient will automatically hear it.
5.David says "Hmm ..." (indication that you've picked the right recording)
6.You talk to the second patient, who will now remember something.
(And then you repeat this like 75 times or so
)
Sometimes it can get confusing which recording will trigger which patient's memory, but most of the time it's pretty logical.