If a man and women find out there was a mistake in their Nikah (out of ignorance) and they already had sexual intercourse. Is iddah needed to be observed before correctly reading the Nikah again?

Chapter twenty-nine » Miscellaneous rulings on divorce
Ruling 2554. If a man has sexual intercourse with a woman who is not his wife supposing that she was his wife, the woman must observe ╩┐iddah, irrespective of whether she knew that he was not her husband or supposed that he was her husband.

What does this ruling mean then?

No. Ruling 2554 talks about a woman who is married to another man.
In your case, the sexual relation was with the same man, and it was not fornicate. Hence, there is no need for iddah.