When connected to a remote machine, you are working directly with that AutoMate Server. Therefore, if you select a managed task and click the Run button, the task will run on the remote machine, not on the local machine. You will, however, still receive failure and error notifications locally if you're Task Administrator is set to do so in its local options.
To run a task a "remote" task locally, you first need to copy or move the task from the remote machine to your local machine, and then run it from your "Local Tasks". This can be done by selecting the remote managed task, selecting Copy or Cut, then highlighting or navigating to your Local Tasks (using the Task Folder is easiest) and Pasting. Then, run the task. This method also works for moving a managed task and its associated task file to your local machine.
See Also:
What is Remote Administration?
Configuring Remote Administration