Well, I went back to playing after I posted this. I turned on my "Salvation" and my "Cavalier" (Which I had forgetton to turn on in the last battle with the lvl 7 mobs) and with just the first swing, I got a conviction....
I guess I'm still confused why those two abilities had to be turned on for me to get convictions.
Also, thank you for your help.
I don't mean to be rude, but you really should read your abilities' descriptions.
Salvation does not affect convictions at all. It should be on regardless, but it is not what generates your convictions. Salvation causes your attacks to heal you; the description has more technical details.
Cavalier is the buff that grants you convictions for using life based-damaging abilities. Most of the Justicar offensive abilities are life based, and so most attacks will generate a conviction while this buff is active. Without this buff you will not generate convictions, because no abilities generate convictions by themselves.