Your resources are not getting email notifications when a new Task is assigned to them.
I have checked off “I receive a new task assignment in my projects” for “Manage My Alerts and Reminders” as below:
And that might not be enough. You need to check off “My project tasks are modified” as well.
And the reason for that is you might be creating a Project with “n” number of tasks, and then assigning them at a later point in time. At this “later point in time” Project Server thinks this is not a New Task (or Assignment), it thinks the Task (or Assignment) is modified – in which case the second checkbox comes handy.
This is pretty annoying since some of the resources dont want to know what’s going on every day with their tasks, but rather want to know only when NEW tasks are assigned to them.
Not sure if this is a BUG or BY DESIGN. I will investigate and update this post.