The book indicates that you can change the item distributor mode to random by right-clicking with an environmental eye equipped. Looking at the item distributor with the environmental eye equipped shows the hopper icon indicating that it's in equal mode, however, this does not change at all when right-clicked on with the environmental eye equipped, there is no indication that the block was right-clicked with the environmental eye equipped such as the arm moving like it does when opening chests, and the mode does not appear to change, still distributing items equally between the chests in a round robin fashion as before.

Versions:
Minecraft: 1.18.2
Forge: 40.1.84
Nature's Aura: 36.3
Patchouli: 71.1

Cannot reproduce this in 1.19.2. Please try to see if this still happens, as 1.18.2 isn't maintained anymore except for gamebreaking bugs.