The key locks in the doors aren't linked to the central locking or the alarm, so at least that bit is operating as it's supposed to.
With the alarm, I'm not sure if you're on about unlocking with the key or the remote, but the alarm will definitely go off when the door is opened if it's unlocked with the key instead of the remote.
The remote is the only way to operate the central locking from outside and disarm the alarm.
Our ZJ is a bit weird in that the central locking switch inside the car will arm the alarm if you lock it with the engine off - I've caught myself out a few times when sat in dodgy car parks.
Jay can confirm that ZJs definitely do come with an audible alarm!