Hi,
That's probably because you're using the "simple date picker (obsolete)" instead of the "advanced date picker (recommended)" type in your custom field.
The simple date picker uses Joomla's date picker system and it has some backward compatibility issue with recent versions of Joomla 3, which lead to that kind of display error.
That's why we have the advanced date picker, which on top of having more options works fine with all the versions of Joomla.
The simple date picker is kept only for backward compatibility on our end (so that people with old versions of Joomla can keep using it) and you should avoid using it.