Tasks synchronisation without the "MySite" feature

Hello Everyone !

First of all thank you in advance for your help ! 

I have an issue with tasks synchronization. 

In my coprorate SharePoint, the "MySite" feature is unavailable, so I can't use the button "synchronise [tasks] with outlook" .

It seems that there is a solution.

When a task is assigned to someone, the person concerned receives a notification by mail and a button "Connect with this tasks List" (at the top left of the email) allows to synchronise the tasks list.

One of my colleagues send me the email he receives when he has a notification task :

I don't understand why this button doesn't appear on the mail notification when I assign a task from my SharePoint : 

I checked with my colleague SharePoint : the same features are activated and MySite is also unavailable.

Hope someone can help me :)

Thank you again!

Marie.