I've never had the seat come out of the front lock tabs, but it has to be one of the worst seat designs out there

With the seat properly fitted it shouldn't move fore and aft, the bit that stops this is the lock at the rear. You have to lift this when removing the seat.
As 54K said check that the tabs are in place. The best technique I've found for fitting the seat is to use one thigh to push one of the flappy ears towards the bike, use one hand to pull the other ear in, then you can use your remaining hand to pull the seat forwards and push down onto the lock. the check the flappy ears are secure in the tabs.