Sold iPhone, reset but didn't sign out - no longer in Find My

Hi,

I just sold an old phone, I used 'Erase All Contents and Settings' but I didn't sign out of my Apple ID beforehand.

I've now read that you're supposed to sign out or the new user may have difficulties using it. However, when I did the reset I received an email from Apple stating that Find My has been disabled on that phone, and the following text:

"With Find My disabled, this device can no longer be located, placed in Lost Mode, or remotely erased using icloud.com/find or the Find My app. In addition, your Apple ID and password will no longer be required for someone to erase, reactivate and use your iPhone."

I read this to mean that my ID isn't still on the phone and the new user shouldn't have any issues setting up, does this sound correct? The phone definitely isn't in my Find My list anymore. I'll hear from the buyer tomorrow if there are any issues but I'd like to prepare if it's going to be a problem.

Thanks!