Is there a way to determine if cell is a date?
I know about style.getDataFormatString() but that doesn't help me,
because I can't determine if is formating is for date or not.
If you're using the XSSF UserModel, then you want DateUtil.isCellDateFormatted(Cell) - this will return a boolean telling you if the format string for the cell represents a data or not.
If you're down at the low level XML stuff, you need DateUtil.isADateFormat(int,String) instead. The style ID comes from the cell xml. The style string you'll have to get out of the styles table, which is a different Package Part. There are helpers for loading that though
You probably want to look at XSSFExcelExtractorDecorator from Tika for an example of doing the latter - it does formatting of cells from an event parsing.