Is the damage applied at the same time. (Draw if both your life points are low) Or you take the damage first then your opponent. (You lose before your opponent takes the damage if the effect dame is high enough.)
as a general OCG rule:
if you activate any card that make both players take damage at the same time you will take the damage first and if your life point hit zero you will lose.
this also goes for skills as duelinks follows OCG rules.