Where they live it's a very wet/high humidity climate. Moss will grow on you if you stand still. They are also using concrete mix and a mortar mix for most of their work.....pretty sure. Though I do think they gave a demo a long time ago on Martha Stewart using hypertufa.
You want to use chunky bits of compressed peat moss in your recipe. Do not sift just break up into small pieces. You can stick moss to fresh hypertufa. Just use a water bath to leach out the lime. Make hypertufa bowl, unmold in 24 hours, clean up (gently use wire brush to rough up inside and outside) and rinse off, put in plastic bag overnight, remove from bag and put in a water bath (plastic tub full of water to cover the bowl) for 3 days, change water every day. It will be almost completely cured by the 5th or 6th day. Remove from bath and apply your sheets of moss to the bowl. Press into the bowl to push the mud on the back of the moss into the crevices left by the peat moss that washed out. Set bowl in shallow pan of water to aid in keeping the bowl and moss damp. It will adhere if you keep it damp and in the shade. Make sure you gently rinse the moss once it's set. This will remove any mud that's still loose. Once it adheres, make your fountain. This does not take 3 years. Have fun and let us know how you make out.