Apparently you can only have one stacking sigil type buff at a time. Whichever one activates first will be the one you have until you are downed, log out, or whatever else removes it (I think that’s it?).
This is no matter what weapon or weapon set the sigils are attached to. I have the condition damage sigil on my main hand scepter first weapon set. I have the power sigil on my main hand dagger of my second weapon set. They never stack together.
If this is working as intended or not is the real question now. If it is, there needs to be more warning/explanation before applying them or on the tooltips themselves.