I know that food poisoning isn't instantanious having been through it myself

but it still raises the question how long was the family at the restaurant and how soon after the kids began eating did the "event" happen in the parking lot? If they spent some time there it may have been long enough to produce a reaction.
The other question to be asked is what did they eat say an hour prior to getting to the restaurant, that could be the culprit as well.
But given the lack of concern by the manager over the condition of the kids I'd still alert the health dept that something happened and let them investigate.