You should've checked the build number before and after updating.
From what I have heard, all currently arriving iPhone 13 have iOS 15.0 build 19A345 installed. The update you are getting is one build newer (most likely the "pegasus"-fix), updating the build to 19A346.
15.0 that was released to the public on September 20th already had build 19A346, but that release came obviously to late to be loaded onto the iPhone 13 devices ready to be shipped.