I built this and it worked fine. I set the repeater to 2, 3, and 4 ticks, all worked. I can't really tell what's the problem because the video doesn't show all the redstone in action when the button is pressed.
My assumption is that you are experiencing a bug that has to do when redstone travels through different chunks (redstone sometimes isn't consistent in different chunks, not sure why). However, when I built this having the redstone going through different chunks it turns out this is not the case. I don't really know the chunk borders look like in this video either so I'm 100% what the problem is.
Also yes, this seems like a bug. Can you perhaps send another video/picture of the bug in action at a different angle? With chunk borders if you could.
Thank you for your answer. It's all in the same chunk. I filmed it again in different angles:
I'm in the version 1.12.2 maybe that's the problem?
Sorry for the late reply, the version 1.12.2 is most likely the problem.
I can't really tell what the bug is here, maybe something to do with redstone priority, redstone with different powers have different priorities (meaning the order things are activated within a single tick) that is even effected by east/west/south/north but that doesn't seem like the likely problem.
If you insist on 1.12.2, which you probably are because it's a pretty stable version for a lot servers, try building it in different orientations or different chunks because different chunks processes redstone differently. Redstone is surprisingly inconsistent but understandably so, it's hard to get a perfect set of rules that allow redstone to be consistent in single tick and orientation.
It's obvious the problem is with the redstone torch not picking up the signal fast enough, try this:
After the one tick pulse put two repeaters set to two ticks (one position up) and make the rest the same. It might be a problem with the repeater giving out a less than 3 redstone tick pulse because the initial pulse was so short and hopefully the second repeater will fix it.
If the problem persists, then maybe you do need stick with the slow and agonizing three tick repeater ;(