In the photo below you see three whistles, and the tone ring goes from fully open but in place against the mouthpiece to nearly completely closed.
The effect of the tone ring in these three positions is as follows:
Fully open: In this position the ends of the tone ring and the lower end of the mouthpiece form "walls" around the sound window of the whistle. This has the effect of organizing the air a little bit for the low notes. The whistle speaks it's loudest, and is pretty clear, with a hint of chiff, and a nice fruity finish. (No, wait, that last fruity bit is for wines.)
Partially closed: A little breathy sound is introduced, and the volume is slightly reduced.
Mostly closed: The whistle is quite breathy, almost whispering it's notes. A little more open than this and it sounds somewhat like an original Clarke.
Removed from the windway: This position is not shown, but the tone ring is simply slid down the body an inch or so from the mouthpiece. This takes the tone ring completely out of the sound producing process. When this is done, the upper notes of the second register are a little easier to sound, and the overall sound of the whistle is a little cleaner, or less chiffy than with the tone ring in place. The trade-off is a weaker low end, requiring a little more care to sound the bell note.
Regardless of the position of the tone ring, my whistles play easily in both the first and second registers, and the octave jump is easy to control. No whistle plays itself however, and a complete beginner - that is one that has no experience with breath control - will still have to learn to make the whistle do what they want with respect to octave jumps and accurate tones for the various notes.
A little more about this last point. If you can whistle with your lips, you will notice your mouth cavity changes shape and/or volume (size) when you whistle from low notes to high notes. A similar thing must be learned to play the whistle. Your head is actually playing a part in the production of the sound. You can't put it all on the whistle. But this is good news, as you have the ability to be expressive with your playing using this to your advantage.