The plume could be very hot and rise as it leaves the plant (e.g., as steam rises), as was the case for the Chernobyl accident. If this occurs, the population close to the plant may be spared many of the consequences as the plume passes overhead.
The plume could be released continuously over a long period, or it could be released as a very short puff.
As the radioactive plume (cloud) moves away from the reactor site, radioactive materials will settle out and deposit on the ground, trees, people, etc. This is called ground contamination.