Hmm. That should be the correct method, even if the user has admin rights.

The restriction wont prevent it from launching though, and in my testing it kills it after 10 seconds or so, but you have to make sure that you set it to Quit the application.

I have my restriction send a message that Mountain Lion is restricted at this time.

That is the correct process to look for. We just added it in this morning and its working for us. Make sure to run a 'sudo jamf manage', as that pulls down any new restricted software settings.
Mark is correct, the Installer will launch but should be killed within 15 seconds as the LaunchDaemon sees it in the process list.
Stupid question, but you did make sure to check off one of the boxes, such as "Kill Process", right?

If I already have a Restrict Software set to look for the Process Name "Install Mac OS X" that should cover both 10.7 and 10.8, correct?

I'm not sure about that. The name changed slightly. For Lion it was called "Install Mac OS X Lion.app". For Mountain Lion its just "Install OS X Mountain Lion.app" Note the missing "Mac" part. I'm not clear on whether Restricted Software would catch the new one or not.

No, Apple dropped the "Mac" from "OS X" in Lion and Mountain lion

Specific process name for 10.8 is "Install OS X Mountain Lion"

@mmdowjones - I agree. To cover 10.8 installer, the process name is "Install OS X Mountain Lion".

Now I have two Restricted Software entries:

First:
Display Name: Restrict pre10.8 Installer
Process Name: Install Mac OS X

Second:
Display Name: Restrict 10.8 installer
Process Name: Install OS X Mountain Lion

Nicely combined with an exclusion for smart groups who have purchased the upgrade (excluded from the restriction).

To do this, we made a static group for the machines which can legally apply the update, then a smart group picks up when the installer is cached. Users can then Self service the rest of the process.

Listing Install OS X Mountain Lion.app as the process to look for works for me. It didn't work when I excluded .app from the process name.

Thanks guys. Will test this again tomorrow after I restore my machine.