How did the execution of the Rosenberg's lead to the beginning of the end of the Second Red Scare?

I was just reading about this case on the Internet, and I came across some websites that said that the Rosenberg’s execution led to the beginning of the end of the Second Red Scare. I really don’t understand how it led to the end of the Second Red Scare or let alone the end of McCarthyism. Didn’t people at that time get even more scared of communism due to this case?