This is something I wanted to report to @lilwhitemouse as it might be a compatibility issue:
The Pushers from Industrial Rollers at times do push items into storage buildings (crates, dumpster, ...) but at other times it doesn't. I think it has to do with how buildings, once filled up to a certain level, put stacks on all the physical tiles it occupies, making the Pusher think the building is full. This is just speculation on my side, though, and I'm not even sure which of the two mods (this or Industrial Rollers) would have to fix this.

Who does Industrial Rollers anyway? It's very likely a conflict with how it checks if it can push. Is the code available online somewhere?

As far as I can tell, it isn't open source. As for who develops it, the workshop page is owned by "historic" and there's a forum post[ludeon.com] under "historic_os", and looking at both, I don't see anyone else involved. And yeah, I already suspected it's something on their end, but perhaps it's something you can patch in which might also prevent this incompatibility with other "unusual" storage solution mods.

Does it ever push more than one on each building? Does it ever push more than 2?

...from a realism point of view, you'd need some sort of robotic arm or something to stack stuff into Storage. I don't know if the rollers have those... but people do let dogs haul hay to haylofts, so whatever ;)

I've done a bit of testing:

https://i.imgur.com/DYdaiFR.png
I set up 3 tracks, and put 6 granite chunks on each track.

• The pusher with the A4 chest ends up with exactly 1 chunk on every physical tile
  
• The A4 and A chests do nothing, seems like rollers can output to stockpiles but not storage buildings?

https://i.imgur.com/siHN0RA.png
Then for the top track, I destroyed the crate and one of the chunks, stacked several chunks in one tile, then replaced the crate. Pusher moved a single chunk into the freed up tile. Seems like it works purely in a "find an empty tile that's part of the building" kind of way. The filtering works fine though, as the Pusher only does it job if both the Pusher and the storage building's Storage filters allow the item on the roller.

https://i.imgur.com/siHN0RA.png
I also did a test with stackable items, and added them in groups of 25 (or more, if I clicked fast enough) and those would get "properly" stacked into the storage building, but again only if there are free/stackable tiles left.

As for realism, the Puller and Growing zone puller somehow "teleports" items to its output, so I'm sure having it be able to stack stuff in a box isn't that unrealistic ;)

As for realism, the Puller and Growing zone puller somehow "teleports" items to its output, so I'm sure having it be able to stack stuff in a box isn't that unrealistic ;)

Haha!

Okay, looks like it's exactly a result of the way Rollers does its check. I'll suggest a possible fix to them, but it'll all be up to them to deal with it.

Here's their thread: https://ludeon.com/forums/index.php?topic=26967.msg474208#msg474208