It will increase from 0 to 10 very quickly and go back to zero. I tried placing a couple of them and every once and a while ONE car will deploy to look for survivors, is anyone else having this annoying glitch? Only the 3 helicopters are working for me.
This question is old and it is possible your problem has been resolved by now, but I will put forth my findings anyway!
There are a couple of potential causes for your issue.
If you are using the auto bulldoze mod, you need to turn off burned buildings otherwise the disaster units will not search the rubble. You can also get this version of auto bulldoze which is updated to work with the Natural Disasters DLC.
If the roads are damaged and the ground vehicles cannot get to the disaster site, they will not leave. With that being said, helicopters should still deploy.