I hate to be the one getting this back on topic, but here we go...
H/R Should clear this up. FedEx Freight uses messaging as the communication method of choice (at this time). The fact that dispatch doesn't keep up with these messages in a timely manner (their job), is NOT your fault. Proper leadership can teach them the importance of timely communication. Again, it is part of their job.
You never have to bring your phone, turn it on, or feel obligated to use it. THE DISCOUNT from a phone service carrier is provided by that Company, NOT FedEx.
There are very good reasons for NOT using your phone to notify customers, especially residential. Call backs from suspicious spouses, general complaints, etc. are real, and eliminated (for you) by the call coming from FedEx.
You can use a phone at a customer, but that seems like a lot to ask, unless for an OS&D issue. Pay phones are a rare thing.
The above comes from experience, not theory. The Hotline (fedex alert line) can insure that you get a true and proper response from H/R, as well as followup for all parties. Documented.
Keep us posted.