Since they can log the depth they must have some kind of pressure sensor. They simply check that value once a second, turn on if more than 1 meter under water or go to sleep again for one second.
The metal contact are probably to detect salt water or sweet water because the two have a different resistance. It's possible that they use the same sensor for turning on but then it would turn on as soon as you have contact with water and not wait till your 1m deep.