Hitler's apoplectic rages were well known to those within the inner circle, although he crafted a careful aura around himself as to his public persona (see here as regards his private, not raging like a maniac voice). The infamous scene from "Downfall" which you reference is fairly faithful to the accounts we have from the bunker as the script is heavily based on testimony and memoirs from the survivors of the Bunker. It should be noted though, that that particular spate of anger, which is abbreviated for the film and lasted roughly half an hour, was described as being even beyond the norm for Hitler's anger sessions, screaming about all those who he had seen as betraying him. Kershaw aptly describes it as a "storm [that] had been brewing for days", finally unleashed by news of Steiner's failure to attack as ordered.

It is also particularly notable since, while those who read between the lines have tried to suss out what Hitler really felt about the direction of the war, it was only at this point on the afternoon of April 22nd, with the Soviets moving into Berlin and the city in ruins around him, that he finally openly admitted to those around him that the war was lost, collapsing into tears once his anger could no longer carry him and the "storm subsided".

So to directly answer your question, while the scene from Downfall is portraying a particularly extreme outburst of anger from Hitler, especially in the later years as things no longer went his way, such incidents were more and more common, and well documented by those who survived to give their recollections.

Kershaw - Hitler: 1936-1945

You have to understand that while Hitler was certainly a fiery speaker and a dramatic figure in his life in the public realm, that many of his actions were deliberate to create a certain image of him as a man devoted to his country and a strong central leader for the country to follow. His behavior also changed between the pre-war period and the end days, as a combination of psychological stress and questionable medical treatments by his physician, Theodor Morell, took their toll. So while "Downfall" certainly captures the last days of Hitler and his Reich as authentically as most surviving witnesses can attest, for the most part Hitler behaved in a manner that he thought would be advantageous to achieving his personal goals. While he was called a Teppichfresser (invoking the image of a small angry dog chewing up the carpets) on several occasions, this was mostly a description by detractors who more often than not did whatever they could to disparage the regime (assuming they were out of the reach of the SA or the SS, at least).

Hermann Balck, for instance, wrote that in his encounters with Hitler that there were only two times someone yelled, and neither time it was Hitler. His first encounter, for example, had Hitler being jovial with the local military units, and easily able to get along with the common troops (cracking some jokes at the Gauleiter's expense). Later on, Balck mentioned how when he was describing a military situation Hitler had placed his hand on his shoulder, and described the experience as if he had been under a spell.

Lloyd George was thoroughly impressed by Hitler when he had first met him, and was impressed by his hold on the German people, little aware of the legions of stormtroopers and bureaucracy that held the system together, even describing him as the "Greatest Living German." While his opinion of Hitler deteriorated with Anglo-German relations, it suffices to say that Hitler knew his man and was prepared to act according to however he deemed necessary to achieve his goals, whether it be to play the clown or to be an angry demagogue. And though popular opinion portrays him as the bellicose madman as seen in theater, one certainly could not create the kind of loyal cult that followed Hitler simply by being the loudest shouter.

The stereotype of Hitler as a choleric is an old one.

The stereotype mainly comes from the way he delivered his speeches. He had a persona on public occations, which was different from his private person (as other posters noted, he privately also got more choleric the longer the war dragged on). The way he speaks, the way he gestures, the whole Hitler changes into an calculated explosive, outraged, angry, screaming agitator. This was/is parodied quite often, for example in The Great Dictator (1940). That the way Hitler spoke, with his rolling Rs and general Bühnendeutsch plus South German accent sounds quite angry to most people, doesn't help.

There were also legends of his (real) fits of rage in Germany as early as 1941, recalled by Klemperer in his book LTI: Notizbuch eines Philologen:

Im Herbst 1941, als von einem raschen Kriegsende keine Rede mehr sein konnte, hörte ich viel von Hitlers Wutanfällen erzählen. Erst waren es Wut-, bald danach Tobsuchtsanfälle, der Führer sollte in ein Taschentuch, in ein Kissen gebissen haben, dann hatte er sich auf den Boden geworfen und in den Teppich gebissen.

In the autumn of 1941, when a quick victory was out of reach, I heard a lot talk about Hitler's fits of rage. At first it were fits of rage, then temper tantrums, the Führer is reported to have bitten a handkerchief, a pillow, then thrown himself on the floor and bite in the carpet.

The reason for this calculated use of outrage and anger is the blueprint of the typical speech of Hitler.

At first, he defines a deficit, then he identifies and attacks the "guilty ones", then he says the listeners how they can help him which molds him and the listeners into a great collective.

The arc of suspense is made in a way that the attack on the guilty ones is just before the highlight of the speech (the unification of Hitler and the listeners), the stronger the outrage about the deficit, the stronger the attack ON THEM, the stronger is the binding OF US afterwards, which was the objective of the whole exercise.

It's the same when he talks to the Generals of the Reichswehr as it is when he talks about attacking Poland, as it is when he talks after the 20 July 1944.

TL; DR: As Hitler was calculated outraged and angry in his speeches a lot, it got inferred rather quickly that he privately was a choleric person, so maybe the fits he did have got blown out of proportion as early as 1941.