For a hub-and-spoke style network (along with high-speed data communications) you'd have crews on standby for their legs in the tender ships waiting for the arrival of current inbound leg(s). Some worlds would be waiting for a single arrival vessel while others could have two or more x-boats as part of their portion of the network.
Local data would be continually uploaded to the next x-boat while the crew is simply on standby. Once arrival of the x-boat(s) happens the data should get transmitted either to a relay facility or directly to the tender. At that point the crew would be notified of the arrival and begin prepping for their departure. They should easily have an hours notice - so the real factor may be boredom, boredom, gotta launch! So much like pilots on alert status in the military.
In the Merchanter books by Cherryh the merchant ships themselves were the carriers of data - they would get continual updates from the departure world as they made their way out-system and then when they arrived they would do a data dump while they made their way in-system. For FTL (or sail travel) it's simple and it works. Ye olde sailing ships had much the same process - except they used wax seals on letters instead of encryption algorithms to know if anyone had tampered with the data.
X-boats make sense for the pony-express route and regular freighters for all other data. Specialized mail ships would really only be needed for physical packages. Imperium could save a bundle if they adopted 20th century postal technologies and processes.