In answering this question, it is important that we realize that there is no way to objectively know what causes human beings to have certain attitudes.  We can speculate about what things would have caused this fear of communism, but we cannot know with certainty.  That said, there were many factors other than fear of immigrants that likely factored in to the red scare.

It is definitely true that there was a fear of immigrants in the United States at this time.  The “New Immigrants” were from different countries than previous immigrants had been and they seemed threatening to many Americans.  This is what led to the immigration restriction laws of the 1920s.  It also surely played a part in causing the red scare.

However, there were many other factors that were involved.  First, there was a general discomfort with change in the country.  American values and attitudes were changing in the “Jazz Age” and many people were uncomfortable with that change.  Second, there was labor activism that seemed to many to be excessive and to be communist-inspired.  These included high profile events such as the Boston Police Strike and the Seattle General Strike.  These did not involve immigrants as the main leaders and yet they were frightening to many people.  Third, many immigrants held radical political beliefs.  It is hard to blame fear of immigrants per se for a fear of immigrants who held specific political beliefs.  We must distinguish between these two just as we must distinguish today between anti-immigrant views and anti-illegal immigrant views.  Finally, the Bolshevik Revolution had occurred in Russia very recently.  This, too, had little to do with immigrants but would have been frightening to people who could reasonably fear that it would spread to the US.

There are, then, many other factors that can be credited/blamed for the red scare.  It is impossible to know with certainty which factors were most responsible.