The wet/dry season differs within the Amazon basin depending how far south/north, east/west you are. In the upper Amazon basin around Iquitos, Peru, we have a bell curve of water level in the Amazon River by Iquitos (see graph), which peaks the end of April. Water level is determined by melting snow and glaciers in the Andes Mountains, especially from the huge glacial mass in central Peru known as the Cordillera Blanca.
The hottest time of year is when the sun is directly overhead upon its return from the Tropic of Capricorn, which is near the first of March. The water from the snowmelt takes some time to flood the Amazon basin around Iquitos, so we start to see the seasonal flooding of the lower ecosystems of the Amazon forest in late March, reaching its peak of flooding by late April.
As the seasonal flood spreads through the forest, the probability of rain increases due to evaporation/condensation. In April and May, we may have 65% chance of rain at some point during the day (usually late afternoon), while in September and October the daily probability of precipitation falls to about 35% (usually late afternoon storm).