I use Apple sync on all my devices including my computer and it does delete from one device to another IF you have sync set up properly. And it’s not instantaneous, it happens when the cloud sync happens. When the computer is off or in sleep, it’s not syncing and once it’s woken up, sometimes it takes a minute to sync up. My guess, it was either not set up right or it hadn’t sync’d yet.
Other possibility, he didn’t know about the deleted folder where deleted messages sit for 30 days unless you clear it (like a computer trash can).