(edited by Ragion.2831)
On Crit Sigils Shared Cooldown
Cooldowns are not shared unless you are trying to use two of the same sigil.
The wiki answers questions like this (as well as many others):
https://wiki.guildwars2.com/wiki/Sigil#Sigil_interaction
In general, the two sigils will both provide their effects independently as long as the base sigil is different. The exceptions to this are the attribute increasing stacking sigils: only one stack effect can be active at a time. Additionally, sigils with the same base sigil will share cooldowns between weapon sets.
There is even an example covering the question:
A warrior with Fast Hands is wielding a greatsword and axe/mace, with Superior Sigil of Battle in both weapon sets. He can swap weapons every 5 seconds, but the sigils will trigger only every 9 seconds, since they share cooldown.
Or if you don’t want to parse the wiki: yes, on-crit sigils are supposed to share cooldowns when using the same ones on two equipped weapon sets.
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