That’s what is assumed. But in reality it runs after the started process stops.
That makes sense to me personally. What would be the more intuitive design in your mind?
Maybe think about it this way: ExecStart is what the system will run to transition the service from the "starting" state to the "started" state. ExecStop is what the system will run to transition the service from the "stopping" state to the "stopped" state.
For a service with RemainAfterExit=no (the default), you enter the stopping state right away once the processes that got started in ExecStart exit. That's useful when you are starting some long lived process as a service, and in that case there is usually no need for an ExecStop. But semantically, ExecStop has the same meaning either way -- it's what needs to be run, if anything, to transition the service from the stopping state to the stopped state.