What you describe is very similar to what the handbook says should happen if you unlock the car with the key. That is, using the physical key apparently doesn't disable the security alarm, which will sound until you turn the key in the ignition. That seems a bit odd to me, but that's what the handbook says. But if you're using the keyless facility that shouldn't happen. Clutching at straws here, but I wonder whether the battery in your key fob might be discharged sufficiently that it unlocks the doors but doesn't send the "disable the alarm" signal? Maybe try changing the battery in the fob, probably a CR 2016 or 2032, widely available?