Yeah. You just roll when someone is brought to zero wounds.
Hopefully this clears things up rather than confuses them:
If a fighter has 1 wound, all unsaved damage would cause an injury roll.
(1 damage vs 1 wound = 1 injury roll,
2 damage vs 1 wound = 2 injury rolls
*3 damage vs 1 wound = 3 injury rolls)
The key part to remember is that the roll occurs when they lose their last wound, which is more complicated than it sounds as you have to keep track of how many wounds remaining, rather than looking directly at comparing the number of wounds remaining versus the number of damage dealt.
If a fighter has 2 wounds and takes 2 damage, the first damage, the first damage takes them to 1 wound, and the 2nd takes them to zero - one injury dice is rolled.
(One damage versus two wounds leaves the model with one wound and no injury dice rolled)
An easy way to work it out/remember, is to remove wounds until a fight has one remaining, then go from there.
A fighter with 3 wounds, taking 5 damage,
will lose 2, and be on 1 wound remaining,
with 3 more damage to come.
*3 damage vs 1 wound = 3 injury rolls.
Where it gets confusing is human brains see:
”i have 3 wounds, i take 5 damage, that is negative 2, so two injury dice” Nope!
5 damage versus 3 wounds, remove 2 (down to 1), becoming 3 damage versus 1 wound remaining.
Confused? Yeah, especially during the heat of battle when dice have been rolling off the table and everyone has been laughing and joking around.
Just remember:
only after the last one is lost