task owner should get an email notification. Go to team site => Tasks list => List Settings => Advanced Settings. You can find
an option to enable the send email notification.

In this blog you will see how to enable send email notification in SharePoint Tasks list using powershell.
Powershell Script:
$site=Get-SPSite "https://serverName/sites/Vijai/"
$web=$site.OpenWeb()
$list=$web.Lists.TryGetList("Tasks")
if($list -ne $null)
{
$list.EnableAssignToEmail =$true
$list.Update()
}

Satish BabuPosted Aug 13, 2015, 12:18 AM
Hi Team, Even though we tried the above script it is not working and we checked the outgoing email settings everything is fine .. could you please help us with this issue...