In a nutshell, this is what Remote Buddy does to determine which application to control / which Behaviour to pick:

1) Check the currently active (in terms of "input focus") application: if there's a behavior for it, it gets picked. If not, it proceeds with 2).

2) Check which applications are running in the background: if there's a behavior that supports background control of a running application, it gets picked. If not, it proceeds with 3)

3) Switch to the Default Behaviour.

When Finder is active - or Flash Player leaves the context of its host and runs its own process for fullscreen display - no matching Behaviour can be found for the currently active application and Remote Buddy advances to step 2. If you happen to run iTunes at the time, chances are high, it gets picked in step 2.

I don't know how Rowmote Pro works, but when I understand you correctly, you have to manually select which application you want to control. Whereas Remote Buddy, by default, does the switching between Behaviours for you automatically depending on which application is currently active.

Remote Buddy does offer an option at Prefs > General > Advanced however, called "Manually activated Behaviours stay active until they are explicitly deactivated". If you enable that option, Remote Buddy will not auto-switch Behaviours whenever you manually switch to a Behaviour via Remote Buddy's menu, but rather stick to that Behaviour until you either manually deactivate it or select another Behaviour. You can also achieve the same via an AppleScript one-liner.

Best regards, 
Felix Schwarz