Damage Over Time (DoT) is a function of the heroes BASE attack stat. Things that affect the amount of DoT damage dealt are:
Card attack stat (i.e. unlevelled has lower DoT than a maxed hero)
Emblems
Troops
Emblems you can see the effect on the hero card in your roster. Troops are only applied between hitting “attack” and the puzzle/board generating… Hence why the DoT in a battle is different from what is shown on the card before/after battle.