Does Safari have something like Firebug
that will allow you to "inspect" the code and figure out what it's doing?
, support doesn't technically cover custom coding. The menu works fine when styled as intended when the design was created; the issues you are having are related to custom coding and aren't covered by support. While I was happy to help up to this point, I have a "no Apple products" policy and therefore will not be installing Safari on my computer.
If Safari has Firebug support or built in Dev Tools, I suggest using it to inspect the menu and play around with the CSS properties. Considering the fact that it works fine in Firefox and Chrome on both Windows 10 and Linux, I'm guessing there's something that Safari is ignoring that it shouldn't.