Correct, Tour, Sport and My Mode are saved through ignition cycles, meaning the car will start up in the mode you last had it set to. If you set it to V Mode, Track or I think it is called Snow mode, then it will start up in Tour Mode at the next ignition cycle.
This is separate from the ability to associate the dash layout display to the drive mode. For example, if you like Tour Mode, but prefer to look at the more exciting looking Sport or Track display you can set it to do so. If you look through the settings you will see that you can select the dash layout or take the defaults and let it change with the drive mode. Another example, is if you like Sport Mode, but prefer the Track Mode display.
Personally, I just set my preferences in MyMode and leave it. I set the exhaust to Track, Brake pedal pressure to sport/middle setting, suspension to Sport and steering to Sport/medium. So, for me, MyMode is basically the default Sport setup but with the exhaust wide open in Track setting. If I am just going for a highway cruise, I will put the suspension setting in Tour mode by modifying MyMode real quick since I don’t like muffled exhaust, light steering and mushy brake pedal of default Tour Mode.
Lastly, I have VMode reserved for those spirited driving moments. I set VMode suspension to Track, Steering is still Medium, Exhaust always wide open, braking I still keep in sport since I am on the street, and I have PTM set at Sport. The MyMode and VModes are nice improvements to this generation. The new C8 corvette gets the same thing, except they call it ZMode. The Camaro and C7 corvettes settings weren’t as flexible.