NO NO NO! They have said the scanning happens on device. It doesn't get reported until it's uploaded to the cloud.
They create the hash on device. They read the 1's and 0's of your photos and create a hash. They then compare that hash to the local database (on your phone) of CSAM hashes.
Sounds like YOU don't understand how it works.
Since you don't believe me, this is from Apple's privacy chief, Erik Neuenschwander:
The hash list is built into the operating system, we have one global operating system and don't have the ability to target updates to individual users and so hash lists will be shared by all users when the system is enabled. And secondly, the system requires the threshold of images to be exceeded so trying to seek out even a single image from a person's device or set of people's devices won't work because the system simply does not provide any knowledge to Apple for single photos stored in our service. And then, thirdly, the system has built into it a stage of manual review where, if an account is flagged with a collection of illegal CSAM material, an Apple team will review that to make sure that it is a correct match of illegal CSAM material prior to making any referral to any external entity. And so the hypothetical requires jumping over a lot of hoops, including having Apple change its internal process to refer material that is not illegal, like known CSAM and that we don't believe that there's a basis on which people will be able to make that request in the U.S. And the last point that I would just add is that it does still preserve user choice, if a user does not like this kind of functionality, they can choose not to use iCloud Photos and if iCloud Photos is not enabled, no part of the system is functional.

Apple Privacy Chief Explains 'Built-in' Privacy Protections in Child Safety Features Amid User Concerns
Apple's Head of Privacy, Erik Neuenschwander, has responded to some of users' concerns around the company's plans for new child safety features that will scan messages and Photos libraries, in an interview with TechCrunch. When asked why Apple is only choosing to implement child safety...