When I was fighting against Hemomancer groups in the Titan’s Wound during story, I noticed that the traits like Heartstopper affected my creatures. I did not check if I gained the actual stats, but the game showed me that I got them because the stat increases and trait name showed up at my creatures rather than at the enemy creatures.
It went by too quickly to capture a screenshot of it, but it happened consistently. I haven’t seen the ‘popups’ happen to my opponent, just my creatures. I assume it shouldn’t work that way, right?