Does anybody know if we can avoid these corner faces material leaking?
Seems to be a bug/problem with the bevel options, try change miter outer option.
miter_outer.blend (116.0 KB)
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For a sharp corner it works but for my needs which I want it to be curved then arc works better apart from that small issue.
What is the blender version?
I understand that this problem has been improved in the higher version 
I used 4.2.0
If you download my example, did the problem exists?
I have no issues with your file.
Maybe the edges are not smooth, so they don’t recognize Face accurately.
fsfsa.blend (121.8 KB)
If you add an edge to make a smoother round, it works properly.
Add…
The cause of the problem is that the edge cut by the Boolean modifier is cut once more in the bevel modifier.
The angle of the option to cut the edge of the bevel modifier is 30 degrees, which is the angle to cut the edge of the round of the box used in the Boolean modifier.
※ I’m not an English speaker, so the explanation is somewhat lacking. 
I find out setting boolean to “Fast” sloves this also.
So it is an precision error!?
It’s not a problem with Boolean Modifier.
https://docs.blender.org/manual/en/latest/modeling/modifiers/generate/booleans.html
Boolean Modifier’s Solver Options are just differences in how modeling is handled.
This is the number of options you choose when there is a problem with the process being processed.
The underlying problem has nothing to do with Boolean Modifier.
I attached the video because it is difficult to explain smoothly. Please refer to it. 
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Yes, now i see what you mean. 
But it is still weird, take a look at this please:
material_bleeding.blend (115.2 KB)
By playing around i saw that boolean with “Fast” does not transfer materials. Confused me.
I don’t know about this issue.
Material setting is possible for the beveled part,
but there is no option to control the problem that occurs when two applied materials are applied, as in the example. (The problem is not a render, but there is a rule. )
This could be a bug or a problem with an unsupported feature.
If you want to check this, you’d better submit a bug report.
Add…
There’s something reported as a bug, but I haven’t found any information that’s been resolved. See link
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Searched a bit: https://projects.blender.org/blender/blender/issues/60302
This is “working as intended” in that the code doesn’t try to be consistent here, and this isn’t a regression. It is more like a feature request to come up with a consistency rule.
I’m sorry, but I don’t have any good idea on how to fix this.
When there are an odd number of segments, it has to pick the material from one side or the other and it is a bit of a coin flip which side to pick. The logic used currently just depends on which edge happened to be picked to begin the list of edges around a vertex. Maybe in particular cases like yours one could propose heuristics like “pick the side with the lowest average z-value for coords” that might put some kind of consistency on, but I have no idea how many such inconsistent cases would be fixed by a rule like that, and how many would need a different rule.I am closing this for now, but keeping this in mind as a feature request. There’s a similar one for consistency of UV splitting, and I may work on both together some time in the future.
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