Do I need to delete an app's related data in ~/Library myself when I delete it?

When I delete an app (move it to Trash) do I also need to delete its related data in ~/Library myself?

A user is not generally expected to delete those file themselves. If you are aware of, and wish to delete them, you can do so. The most that you would lose is the app specific preferences and any user data which could be re-used if you reinstall the app in future.

My second question is is this the main function of other uninstaller tools?

Since you didn't name any tool, this cannot be answered concretely, and would depend upon choice of tool. But a tool that lets you delete an apps' related data is generally expected to show the files/folders that it would affect and should let you choose what items to keep.