Maybe they're snooping to your imessages and use the same apple id so they receive all imessage conversations you have on your phone to theirs.
No , that's not it . They were just looking at my phone , and the texts that were deleted were from an Android phone , so it was a text , not imessage
Is the person looking at your phone and pointing out the missing texts the same person who you are having the conversation with? (had to ask)
Otherwise I dont see how its possible, just deleted some old SMS messages and I dont see anything that would give it away.
only thing i can think of is that they are searching certain words through spotlight. results will show up even if you deleted the message.