A letter via the Cursus Publicus could travel 80-100 km per day, considerably more in an emergency (like Rome on fire). Plinius sent and received letters this way as he was a VIP with an imperial decree to use it. A normal person, like Felix and his family would usually not be allowed to use the Cursus Publicus, and would probably have to pay a messenger to travel the whole route while not knowing exactly where to find the receiver.
In this case it was inside the package that was probably sent to Plinius from his household, maybe via someone else with an imperial decree. That should solve the time issue. I thought about the possibility of it being a forgery, but I don't see Plinius as the type to pull a move like that. Also, Felix apparently doesn't see anything suspicious with a letter signed "Your wife". Maybe that's how it usually was when she hired a scribe to write it.