Creating a second site (in multisite env) with the same user name for mysql lead to "PDOException: ... Access denied

Steps to reproduce de bug:

1. Site1 is fully working, it use "username" and "pass1" to connect to the mysql database (db1)
2. Now, create Site2, with the same user name but a different password to connect to db2

conclusion: Now, site1 is not working but site2 is working properly

Step to confirm that this is a "identical user name" problem

1. Log into the database with root
2. Grant the privileges for username/pass1 for db1 [=for Site1] by entering the following code:
   
   GRANT ALL ON `db1`.* TO 'username'@'localhost' identified by 'pass1';
flush privileges;

conclusion: Now, this is the opposite, Site1 is working and Site2 is not working... If you grant privileges for username/pass2 for db2, Site2 will works again but as you understand now, Site1 will not works...

Note1: The installations of Site1 and Site2 have been made with drush with the following syntax:
drush site-install myprofile --db-url=mysql://username:pass@localhost/db1 --db-su="root" --db-su-pw="rootpass" --site-name="site1" --account-name="site1adm" --account-pass="site1pass" --account-mail="myemail@gmail.com" --site-mail="myemail@gmail.com" --sites-subdir="site1.be" --locale="fr" -y
Juste change site1 into site2 for Site2 install command
Note2: I am a noob in sql stuff, maybe there is a simple sql solution to fix this... but in this case, the documentaion should mention this
Note3: This is maybe a drush bug... I really don't know

Thanks in advance for any hint!