The US also came into those countries with massive reconstruction funds. Injecting tons of money buys a certain amount of loyalty, especially from anyone in those countries who did not support the previous regime or had fallen out of love with it.

We also promised them protection and trade and for some reason generally made good on that.

We didn’t do that with Iran or any of those other countries we messed with during the Cold War. In fact we seemed to not even really care much what happened after the coup. The only objective was to contain communism, so as long as whatever thing took power was not communist it was fine. It didn’t matter if they were monsters or even if they were even more anti-American than the previous regime as long as there wasn’t a hint of Soviet ideology.

We totally overreacted to communism to the point of actually building up more determined and ideologically consistent enemies.