How did the villagers know about Naruto being the Kyuubi's jinchuriki? I know that the villagers of Konoha were afraid of the Kyuubi because of its rampage on the village, and that the Fourth Hokage saved the village by sealing it inside Naruto. Based on this answer, the Third Hokage hid his identity to protect him. 

Did the Third Hokage hide only Naruto's relation with the Fourth, or also him being the Kyuubi jinchuriki? If so, did the villagers find out because Naruto went out of control with the Kyuubi's chakra? 

Edit:
To make clear what I am exactly curious about.

Why didn't they also hide Naruto's identity as a jinchuriki so the villagers will not hate him?
The villagers know that Naruto is the Kyuubi's Jinchuriki because Sarutobi Hiruzen told them!

Here's why: In one of the earliest chapters, Hiruzen tells Iruka that the Fourth Hokage had died hoping the villagers would see Naruto as a hero, who sealed the Kyuubi. The only way Hiruzen could make it happen is by telling the villagers that Naruto was the kid that the Fourth Hokage sealed the Kyuubi into.

However, he decided not to reveal Naruto's relation to the Fourth Hokage. Note also that Kushina's pregnancy was a highly classified information, known only to Hiruzen, Biwako, Minato, a few ANBU members and some others. Hiruzen could have made up a story that Naruto was a random kid that Minato picked to seal the Kyuubi (or something like that), and few would have suspected or questioned him. 

PS: A little plot hole there is that on growing up, Naruto's close resemblance to Minato, along with the Kyuubi story, should have raised a few eyebrows, but Kishimoto probably decided it was not important enough for the "plot" to require an explanation.