I have a 2007 hino, with an Allison transmission, that is probably how your used truck is specked, Hino does have its own brand of tranny called an Aisin or something to that effect but they aren't usually specked for expeditor's at least I have never seen one.
I have 430K miles on my truck and have had NO, transmission problems.
If you have to get an automatic, then the Allison is about the best you can get, they are in fire engines, and defense applications, so I wouldn't worry about reliability.
If you can avoid getting an automatic I would. The automatics weigh about twice as much as a standard, and have higher maintenance costs. My Allison costs me about 1200 a year in scheduled maintenance. Fluid and filter changes. Which if you choose to maintain your truck you will have the same cost.(unless you don't work much)
I have lamented in the past my choice of getting an automatic, but not because of reliability, only because of $$$$.
As far as the Hino truck is concerned, I am overall very happy with it. I have never owned another straight truck so admittedly I have little to compare it to, but I have driven a Volvo tractor, and I had more problems in 110k with the tractor than I have had in 400k with my hino.
Also, I have seen my same truck, for sale on EO for 30K with less miles which in my opinion is a steal. I considered buying it myself, and hiring a team to drive it, but my dislike for employees has stopped me from doing so.
As far as Hinos in general, there are many complainers on EO, however most of them don't actually own one. Most of the things I have seen complained about have to do with "User Error", or stupid mechanics, both of which I have suffered from. There are a couple of people on EO, who have Hino fleets and continue to buy them.
Theres my 2 cents, if you search my other posts you will find plenty of info on my Hino adventure.
