Cyclones can't form near the equator due to lack of Coriolis effect.
Although quite rare, it can happen, as in Tropical storm Vamei in 2001 near Singapore and Typhoon Sarah in 1956. However, it would appear that rotation does not come from the Coriolis effect, so you are half correct, but rather just the right combinations of weather conditions in the 800 to 500 hPa layers and the terrain.
K