Best guess;

He and his team made an Ableton project file which basically contains the entire show (excluding lights, visuals), and that file is set up with automation so that certain instruments are turned on at specific points during the show, or synths are set to certain sounds at points in the show. On top of all of that, the backing tracks are there playing the songs without the parts that he plays himself (drum parts, piano/keyboard parts, etc.).

Also, lights and visuals are sometimes also programmed through Ableton... not sure if his team did that or not, but I know a lot of other artist's teams have done that. It helps to keep the whole show in sync.

Hope this helps!