I guess you're right, as a refresher would imply that you ever understood the difference between a turn and a round. I even posted the rules reference to help you.... here I'll spell it out.
1. You roll for priority and win and take the first TURN in that ROUND... your opponent has the second TURN
2. You cast doom sigil
3. Finish your TURN... count up casualties roll and apply buff it lasts until your next hero phase
4. Your opponent takes there TURN... buff still active count up casualties THEY apply buff it lasts until their next hero phase
5. Roll for priority for the next ROUND... whoever gets the first TURN of that ROUND loses the buff on the targets they chose
6. Rinse and repeat as long as the spell is on the battlefield
Each buff lasts 2 combat phases unless you get a double turn