Why do people tend to react the same way during the Two Minutes Hate programming and after Big Brother appears on screen?

They react the same way because they have to. This is a totalitarian society in which any sign of individuality is extinguished by the state; everyone must think the same and act the same. If anyone shows themselves to be less than enthusiastic during the Two Minutes' Hate they could be signing their own death warrant. Not going along with what everyone else is doing is a deeply suspicious sign to the Party; it shows that you're not fully committed to the goals of IngSoc. In some ways, the Two Minutes' Hate is another way for the Party to weed out potential dissidents and subversives, those who represent a threat to the existing political order and the Party's absolute power. The Two Minutes' Hate is also designed to bind people together, giving them a common object of loathing that will turn their frustrations with daily life in Oceania towards a convenient scapegoat such as Emmanuel Goldstein.
Just as everyone must hate the Party's sworn enemies, they must also love Big Brother. Nothing less than absolute devotion to the supreme leader will do. Once again, everyone must act in the same way, openly displaying their fanatical loyalty for all to see. Otherwise they will become objects of suspicion, paying a very heavy price for their perceived treachery.

To answer this question, take a look at Part One, Chapter One when Winston is describing the Two Minutes Hate. He says:

The horrible thing about the Two Minutes Hate was not that one was obliged to act a part, but, on the contrary, that it was impossible to avoid joining in.

In other words, Winston is saying that Party members do not have a choice about joining in. They are "obliged" to do so; it is non-optional. Failure to join in the with Two Minutes Hate would make a Party member look as though they sided with Goldstein and is, therefore, an enemy of the state. The consequences for this would be severe: imprisonment in the Ministry of Love or, perhaps, even execution.
Secondly, as Winston says, it is almost impossible to not join in with the Hate. The mentality of the majority is so strong that people cannot resist participating. Moreover, Party propaganda has brainwashed these members into believing that Goldstein really is the enemy, so the Hate gives them an opportunity to vent their anger. It is, thus, a cathartic moment.
Big Brother's appearance is almost like being saved from Goldstein and this is why his face is able to bring an end to the Hate.