The short answer is that they don't. Android flat out doesn't support vertical scripts so there's a library that reimplements a lot of UI components. iOS basica

The short answer is that they don't. Android flat out doesn't support vertical scripts so there's a library that reimplements a lot of UI components. iOS basically doesn't, but it's somewhat easier to work around. Chrome and Firefox can render the characters with appropriate fonts, but that can be uncommon and applications using them screw up. Electron apps generally render vertical scripts LTR for example.