The same issues appear in the Chosen demos, yes, in both Chrome and Safari.
I just noticed this, as well, which I have a feeling is related, because on iPhone the comboboxes also default to saying “0 items” — in Search and Filter Pro and in the Chosen demo — rather than the correct default text. This might be because on the iPhone the appearance box is overridden and displayed as an iOS picker?
But what’s different is that on iPhone — but not iPad or desktop — when I use a combobox, it very quickly automatically selects whatever option it’s on. Usually this is the top choice, but you have a split-second where you can slide it down and it will “choose” something else for you. Either way, it’s not very usable. (I have the auto-submit form checkbox selected in Search and Filter Pro’s settings).
Since it’s probably Chosen.JS’s fault, I suppose you probably can’t fix it (easily, at least), but I absolutely love the comboboxes on my desktop site! Could Search & Filter Pro add a setting so that you use comboboxes on desktops and standard dropdowns on mobile (or is there a way to do this with CSS)?