Probably no reason to be worried. The Iberia website and total IT system are notoriously bad. How BA, the dominant partner in IAG, lets them get away with this, I cannot understand. The Iberia IT crew must be really sub-par.
In any case, an incorrect birthdate is probably nothing to worry about. The Iberia website seems to accept just about any sort of data that fits their format. I have heard ("heard" mind you -- I don't really know this person) of someone who has filled in inaccurate birthdays, passport numbers and expiry dates, simply because he/she did not have these documents to hand. There was no problem boarding the flights and no problems at immigration. So I suspect your birthday on the 1st (congratulations!) is nothing to worry about.