Birthdays a day early in Calendar on Mountain Lion
I was having a similar issue for a while using the native Birthday calendar. It's not exactly the same as only the notifications came in one day early. 

To fix this, in macOS El Capitan with Calendar v8.0 (2092.3), I found the following:


Open the Calendar app on macOS
Select Preferences > Alerts
Here change the notification for Birthdays to your choice (in my case "On day of event")


I looked for this option a while ago but was unable to find it earlier. But now with this, I'm neatly notified on the day of a birthday. Perhaps it helps others as well.