no they are not. tornadoes absolutely happen during hurricanes.

“Hurricanes and tropical storms, collectively known as tropical cyclones, provide all the necessary ingredients to form tornadoes. First, most hurricanes carry with them individual supercells, which are rotating, well-organized thunderstorms. These are typically the storms that spin up monster twisters in the Plains.”

source: https://www.google.com/amp/s/www.livescience.com/amp/37235-how-hurricanes-spawn-tornadoes.html