That is indeed correct. The fortune upgrades work a little differently to normal on the AutoSieve.
Each upgrade gives both a chance to generate loot that otherwise wouldn't be generated, and *also* the ability to increase the amount of each loot type granted. The chances of both of these are configurable.
The actual probably are binomial, but a full stack (64) of fortune upgrades corresponds to roughly a 22% chance to get 3 extra rolls, and add 3 of each item type to a stack.
(how did I not find this for the longest time? :))
Anyway, does the artificial hive for the magic bees include Oblivion and Infernal hives? (I haven't tested it out with just those mods yet as I'm putting together a private custom modpack, which ex astris doesn't seem to like).