I found a reason for the first email : to alert the Administrator because the user has to be authorized with private registration.
So I did some more tests and the problem is more about inconsistency with the registration messages sent, depending on the User Registration settings :
>> Public : everything works fine. All administrators receive an email/notification and only if the check-box "Receive user registration notification" is checked.
>> Private : The "main" administrator receive the first email. Him and all other administrators receive the 2nd email. The check-box has no effect at all !!!
>> Verified : The "main" administrator receive the first email. Him and all other administrators receive the 2nd email.
In this case, I don't know why the first email is sent because the interest of Verified is to automate the registration process and not to bother the "main" admin.
If the check-box is unchecked, no messages are sent at all, which is the appropriate result.
So my final question is : do I post this to the dnntracker or am I the only one with this "double" email mess ?
FYI, I use verified registration on my website, that's why I was getting the problem in the first place. My local test site has the default private registration.