Answer
No, the first true animals may have taken a longer or shorter time to emerge compared to the first fungi. The time to a common ancestor is not the time to an origin.
Work Step by Step
Review Concept 32.2 and see that nothing is said about evolutionary rates and times being uniform across different kinds of organisms. For an analogy, imagine your last name is Smith, and you find that you have fifth cousins named Jones. You may have had a common ancestor 200 years ago, but your family name may have only arisen 100 years ago.