EDIT. Oh nevermind i found it:
I guess you were looking for the keymap mode?
Actually, the wiki you link to does not yet fully cover how phrases can be triggered in Redux,
The thing is, Redux has 2 distinctive modes: Program and Keymap. The tutorial wiki only explains Keymap.
Keymap allows you to assign phrases to the keyboard, like you see in the following picture:
...it's pretty straightforward, but also a great limitation in that you can only play a given phrase in the keyboard range it has been mapped to.
Your confusion about the mixture of sounds probably stems from the fact that in the Keymap mode, the keyzone is still active in the "gaps" between phrase mappings.
The Program mode is different, and basically "spreads" the selected phrase across the whole keyboard.
Selecting the phrase is done either via the Redux UI or by sending program-change messages from your host or keyboard.
This is very handy, as you can basically play anything, at any time. And most MIDI controllers are able to switch phrases AND trigger them.
But perhaps the Quickstart isn't too clear on this particular subject - you are not the first to "not get it".
Another user, Satobox, who has offered to translate the quickstart into japanese, has created the following pictures to illustrate how it works:
The program change (MIDI) implementation itself is also quite sophisticated,
as you can switch between all phrase triggering modes (including OFF) in real-time:
For my particular controller, I have mapped program changes 0-7 to individual buttons,
making it easy to switch between (and record) phrases as they are played.