In his brief appearance in the series, Dr. Vulkan does not actually appear on screen, but is only seen on view screens and recordings. He lives on a tropical island with a semi-dormant volcano. It is not shown exactly how he was defeated, but it is shown on a newspaper that he and Trixie start dating shortly after. He has no speaking role.
Dr. Vulkan's only role in the series is in the episode "Emotion Commotion!". When Timmy Turner had earned the reputation as a fearless kid after wishing away all his emotions, he was hired by government agents to track down Dr. Vulkan, who had already kidnapped Trixie Tang and Chester McBadbat in an attempt to lure him to his island. Timmy sees Dr. Vulkan on a screen in his watch, slowly dropping Chester and Trixie into a lava pit. After Cosmo brought Timmy's emotions back to him, Timmy became too afraid to jump into a whirlpool leading to where Chester and Trixie were, but eventually did so anyway at great injury to himself, because his common sense (to just wish Trixie and Chester free) was left behind. Dr. Vulkan is then implied to have been defeated, and is last seen on the cover of a newspaper with Trixie kissing him while he exclaimed about how girls scared him.