The bad news is that, due to the sheer tininess of certain components, iPhones are particularly vulnerable to going haywire in the presence of helium. The good news is that helium just isn't a problem you run into often.
Sure enough, Apple's user guide for the iPhone and Apple watch admits this is a problem:
"Exposing iPhone to environments having high concentrations of industrial chemicals, including near evaporating liquified gasses such as helium, may damage or impair iPhone functionality. … If your device has been affected and shows signs of not powering on, the device can typically be recovered. Leave the unit unconnected from a charging cable and let it air out for approximately one week. The helium must fully dissipate from the device, and the device battery should fully discharge in the process. After a week, plug your device directly into a power adapter and let it charge for up to one hour. Then the device can be turned on again." (Emphasis added.)
