You'd have to format the &return parameter for the logout URL or use a Login / Logout auto action in CB Auto Actions. Below for example should work.

Global
Triggers: None
Type: Login / Logout
User: Automatic
Access: All Registered Users
Action
Mode: Logout
Redirect: [cb:url location="registers" /]

If you don't want to use an auto action you'll need to add the &return to the logout URL yourself. To format the &return you'll need to take the URL you want to redirect them to and base64 encode it then prefix it with B: then add that to the &return in your logout URL.

Do you have a suggestion to cleanly pass this field to the redirection before the log out ?

You don't have to use the URL substitution. You can supply the URL yourself beginning with index.php like the following.

index.php?option=com_comprofiler&view=registers&Itemid=MENU_ID&atid=[cb_codeatid]

Be sure to replace MENU_ID with the menu id for your registration menu item or the URL likely won't SEF nicely if using SEF.

It seems also that a message/alert is not displayed on the registration page (though it works well on other CB pages when we try)

That's a known issue with no fix at this time. Joomla wipes the session where messages are queued so it can't display anything unless the message is queued after the session has been regenerated as a guest session on the next page load, but by then it's too late.