No! You will not experience an Asia-like monsoon, where torrential rains occur for months. However, you should take note of the rainy and dry seasons. Expect intermittent, heavy downpours during the rainy season in all tropical areas. However, those rains are usually not 24-hour, multi-day events. It normally rains a lot during a short period of the day.
Generally, the rainy season is “summer” and the drier season is “winter”. For example, Carnival in Brazil happens during the rainy season in February, which is the summer in Rio. However, the event is rarely affected by the rains. Though south of Buenos Aires and Santiago de Chile, you can expect a pattern as you know it from home with warm summers, cold & rainy winters. Just remember the Southern Hemispheres seasons happen at opposite times. December is summer with July being winter and June having the shortest days.