I have an empty tactical shotgun wielded, a full shell box in the prepaped slot, and Shottyman. Moving doesn't reload the shotgun.
EDIT: I have found
a thread where tehtmi says that this is intended and solved:
This is intended. Shell boxes are a precious resource, and reloading with shottyman is based on your move speed instead of your reload speed. Thus, a shell box would provide no benefit to shottyman-style reloading, so it is usually preferable for shottyman to draw from the inventory.
There is one issue however; if the inventory happens to be empty, then shottyman won't work at all even if the player has a shell box. The solution to this was to allow ammo packs to be unloaded into normal ammo.
I am not convinced. Not knowing this counterintuitive quirk killed me: I ran out of regular shells, equipped the shell box and tried to reload from it. I didn't have time to unload the box. In other circumstances ammo boxes make reloading faster or at least not slower, one would expect them not to delay reloading by several turns.