I resolved this by switching to a multiselect (and hiding the scrollable div) on mobile devices (so no real solution). Thanks for all the help everyone.
Edit: I have finally figured this out. Basically what happened was that after I switched to using a multiselect, it too was acting weirdly in IOS devices when using Safari.
In examining further a colleague of mine noticed dojo touch events on both the scrollable div and on the multiselect (the template I am using uses dojo). I started looking around in the template's source to figure out why these events were being attached to all these elements and I noticed a dojo module called "dojo/touch". After removing this module from the project, the elements are working fine in Safari.
The take away is that 'dojo/touch' and IOS Safari are totally incompatible.