How do you play chess 960 on the app?

When you create a challenge you change the Type to 960

Thanks

How to play chess variants in chess app?

When I tap 960, the board set up looks like standard. I tried it and found that I was playing standard config. What did I do wrong?

You could just create a custom game that looks like 960

On the mobile app or tablet app, tap the button indicating type of game. It is usually [standard] by default. Then tap that button and a list of configurations will appear: look for 960 and tap that.

Creating a configuration manually is problematic because you may set up an illegal one. The site's software generates one of the 960 possible back rank configurations, both sides being the same.