Quote from brid
I really don't think that after just hearing Kushina talk about the 4th's time space jutsu that Naruto would suddenly be able to do it. Hell, even sharingan users have to actually see the move performed before they can learn it, and Naruto has never been anything close to a genius. I think it's more like Naruto just moved really fast and it was supposed to remind us of the 4th, like "oh look Naruto is becoming more and more like him, " rather than him magically knowing how to do the move.
I think it is not related to his father it is more like he learned from the kyubi when he received his chakra.
But also can be a very fast movement (Kisame described that way).