Vasals warfare gives army tradition?

[Autoclave]

I'm HRE emperor with revoked privillegia. I noticed that my army tradition went up while my vassals were doing all the sieging and fighting for me.
Is this how it is supposed to work?

 

[billclintonmask]

I believe you get AT for occupying provinces. So you wouldn't get them from vassals fighting, but when they siege something down you would