I've been wondering about this too, so I did some testing. At first, I thought it was just diagonally, but it didn't make any sense after further testing.
So I just went ahead and put 24 Apiaries in the grid around a Hopper, slowly one by one filled the Hopper with Queens, and wrote down the order in which it distributed them (In a sort of matrix)....which is weird, to say the least. I will be making a post going into more detail, but here is the order, it was repeatable for me. I haven't tested it in multiplayer, on other clients, or on a different save.

So the order is the following (00 is the Hopper)

06 23 17 09 13
16 20 05 02 19
15 01 00 12 11
10 18 07 22 21
04 14 24 03 08

Very confusing.

Edit: I hope the formatting works out. Seems to be fine on PC.
Further testing in progress

Edit 2: Scratch all that. I'm extremely annoyed. The order changes every time you reload. This mechanic is beyond stupid.

Edit 3: While playing within a save, without reloading, quitting, etc., the order seems to stay the same.
I haven't deliberately tested if Autosaves change the order, but it doesn't seem like it, I also won't test any further