We encountered an issue a while ago that notifications aren’t being sent from the My Sites of SharePoint 2013. We first verified we could sent mails from alerts and workflows and these mails were being sent.
Our profile settings were as follows:
We did not set the sender’s email address on the User Profile Service Application and did not checked the “enable newsfeed email notification”. You can set this address on the User Profile Service Application and by clicking on ‘setup my sites’
It can take some time for this to initiate but notifications are being sent from the My Site after this setting.