How do the engines of a multi-engine airplane shut down after fuel starvation?
On multi-engine aircraft the engine on one side is normally fed by the respective tank, so the left engine(s) is fed by the left tank etc... it is possible to cross-feed to allow access to all the fuel in the event of an engine failure.

In order for a simultaneous run down to occur - both tanks would have to have precisely the same amount of fuel loaded and both engines would have to burn fuel at exactly the same rate, which is unlikely.