Model selection (second) tooltip list is obscured by container of the first tooltip

In iOS mobile browser (Safari) the model selector tooltip (second, after selecting the model provider) often (though not always) does not show the full width of the select list options. Could be a CSS z-index issue — the second tooltip list (of models) is limited to the space of its containing / originating tooltip list (of providers).

I apologize if the language is not clear, but hopefully the attached images below better illustrates the problem.