Do I need to change change my Branch integration so that the Branch SDK only fires after the AppTrackingTransparency pop-up?

This is up to you. Our SDKs provide ways to delay tracking the install until after the user has seen the AppTrackingTransparency prompt, but this will also prevent deep linking and we'd only recommend using this delay if you intend to ask permission quickly.

For a full walkthrough of the device-level ads analytics changes Branch is making for iOS 14.5, please read this blog post.