What were the assumptions underlying the us involvement in southeast asia? were they correct?

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!