Problem with Secondary Email Address

I do have 2 Apple-IDs.

Unfortunately, I accidentally added an Email-address to my Apple-ID No. 1, but it should be added to Apple-ID No. 2.

Therefore I deleted it at Account of Apple-ID No 1. And added it as secondary Email-address to Apple-ID No 2.

Seems to be straightforward, but I do not get the confirmation Mail for this Email-Address as secondary address for Apple-ID 2. It still seems to be somehow attached to Apple-ID No. 1.