The locks prevent the latches from opening if the latches are not properly adjusted. If the latches are properly adjusted, they are not likely to open unexpectedly and the safety locks merely provide an extra layer of security. See for information about proper adjustment. The latch mechanism is an "over-center" design which is stable when closed after proper adjustment.
The most likely reason the safety locks don't work is that someone forced them open without sliding the lock lever. This causes a plastic piece (THIS) to break, rendering the lock ineffective. The latch can still be safely closed as long as the latch is properly adjusted. While you're waiting for replacement plastic piece (seen in black HERE), you can wrap a bungee cord around the lever if you don't trust the latch. Once fixed, the lock will work as long as you don't force it. I've had my Tern for 10 years, 12,000+ miles, and have never broken this piece. I understand it was a fairly common problem because of a lot of ham-handed (or maybe just impatient) Tern owners.