No, this is not what's going on at all. The employees never see the original photos in the government CSAM hash database. Apple doesn't even have these photos: it's precisely the kind of content that they don't want to store on their servers. If some conditions are satisfied, the employees gain access to the visual derivatives (low-resolution copies) of your photos, and they judge whether these look like they could plausibly be related to CSAM materials.
The exact details of the algorithm are not public, but based on the technical summary that Apple provided, it almost certainly goes something like this.
Your device generates a secret number X. This secret is split into multiple fragments using a sharing scheme. Your device uses this secret number every time you upload a photo to iCloud, as follows:
1. Your device hashes the photo using a (many-to-one, hence irreversible) perceptual hash.
2. Your device also generates a fixed-size low resolution version of your image (the "visual derivative"). The visual derivative is encrypted using the secret X.
3. Your device encrypts some of your personally identifying information (device ids, Apple account, phone number, etc.) using X.
4. The hash, the encrypted visual derivative, and the encrypted personally identifying information are combined into what Apple calls the "safety voucher". A fragment of your key is attached to the safety voucher, and the voucher is sent to Apple over the internet. The safety vouchers are sent in a "blinded" way (with another encryption key derived using a Private Set Intersection scheme detailed in the technical summary), so that Apple cannot link them to specific files, devices or user accounts unless there's a match.
5. Apple receives the safety voucher. If the hash in the received safety voucher matches that of known CSAM content in the government-provided hash database (as determined by the private set intersection scheme), the voucher is saved and stored by Apple, and the fragment of your secret key X is revealed and saved. (You'd assume that they filter out / discard your voucher if there's no match; but the technical summary doesn't explicitly confirm this; this means that they may store and use it in the future to run further scans).
6. If your account uploads a large number of matching vouchers, then Apple will gather enough fragments to reassemble your entire secret key X. Now that they know your secret key, they can use it to decrypt the "visual derivatives" stored in all your saved vouchers.
7. An Apple employee will then inspect the "visual derivatives", and if your photos look like CSAM (more precisely, this employee can't rule out by visual inspection that your photos are CSAM-related), they will proceed to use your secret key X (which they now know) to decrypt the personally revealing information contained in your safety voucher, and report you to the authorities.
Keep in mind that the employee looking at the visual derivative does not, and cannot, know what the original image is supposed to look like. The only judgment they get to make is whether the low-resolution visual derivative of your photo looks like it can plausibly be CSAM-related or not. Plainly speaking, they will check if a small, say 48x48 pixel, thumbnail of your photo looks vaguely like naked people or not.