Joomla distinguishes between user activation by link through email or via administration backend.
In order to send an email to the user after the activation of the user account one needs to use the link from the email. Activation from the administration backend will not send an email to the user who's account was activated.
What email sending method do you use (see System > Global Conguration > Server > mail settings)? What email sending methods do your extensions use? (e.g. in Acymailing you can configure another mail server)
Do you send email with PHP/Sendmail directly from your webserver,
or use SMTP and send all mail via an external SMTP server?
Maybe the mail is sent ...