Date & time are correct. But even if today's date wasn't correct, if someone's BD in my contacts is Oct 13th, their BD is still Oct 13th no matter what day of the year it is today.
If I hold my iPad & iPhone up side-by-side & go to my Contacts in each. I can click on a person, and under "birthday" it will say their correct birthday on my iPhone, but my iPad will say their birthday is exactly one day later than whatever my phone says. Has nobody else had this issue when they synced contacts to iCloud?