The beta versions of Xcode don't update (automatically or otherwise), and require you to download the full Xcode image for that version.
I believe it's done that way intentionally, so that it is possible for developers to have multiple versions installed at once.
For example, it would be possible to have the current official release (Xcode 6.4) installed for submitting to the App Store, a beta for the current major version (a hypothetical Xcode 6.5 beta) for testing, a beta for the next major version (Xcode 7 beta 5) for testing and Swift 2 development, and another revision of the beta for the next major version (Xcode 7 beta 4) if for example there was a bug in beta 5 that was breaking your code for a particular project.
The command line tools are included in all of the Xcode IDE releases, and don't need to be downloaded separately (they are provided as a separate download for people who need the command line tools and framework/linker stubs but not the full Xcode IDE).
You can select which versions of the tools will be used from the command line by setting it in the "Locations" tab of the preferences of any of the versions of Xcode you have installed.
I think they are automatically changed as part of the updates done when running a particular version of Xcode for the first time, but it's probably best to check in the preferences if you need to make sure a particular version is being used from the command line.