You measure upper margin from top of ascender height and lower marging from bottom of x- height, so you do not account for descender size (the lower extension of charachters like j or g). Seems like FMP Go does a pretty good job with this centering stuff if you measure top margin from top of x-height or lower margin from bottom of descender.
A really big font problem however is the lack of the osx system font Lucida Grande in iOS.
Regardless of the ascenders and descenders FMGO should center text to a button the same as it does in FMP. Unfortunately it does not. This requires developers to make two version of their layout elements if they care at all about the visual appearance of their solution. For a release that was primarily a visual overhaul FileMaker sure did a terrible job in their execution. Their sloppy programming results in thousands of developers wasting their time trying to fix a mistake that never should have made it past their (seemingly non-existent) quality control department.