I only played FOS once while I was abroad, and some things that should have taken longer, like strength training, had been completed. Presumably the game works off the iPhone's timekeeping in that regard.
When I returned, and set the clock back four hours, that's when things started to turn weird. My dwellers have been exploring for a full day and not fought, found or even said anything. The log is simply "00.00 Heading out into the wasteland" or a variation thereof.
Some of my rooms were displaying rush % above 100%, and some rooms were showing 4hr until they'd be ready to collect. And someone who was returning now has 4hrs added on to the time it'll take them to get back.
Not quite sure if there's anything to be done, or if it will right itself over time.