Question

What were the assumptions underlying the US involvement in southeast Asia? Were they correct?

Answer 1

The United States assumed that since the USSR was attempting to spread communism into Asia, countries around the main target would fall as well - the Domino Effect.

The United States fought to prevent the spread of communism by interfering in countries such as Vietnam and Korea - however, both outcomes were unsuccessful or did little to nothing. 

Yes, they were correct as once Vietnam fell to communism so did Cambodia and Laos.

Hope this helps!