Per p. B380, "If you have
zero or fewer HP left . . . You must roll vs. HT
each turn to avoid falling unconscious." The
current turn isn't excepted. You're supposed to roll on being taken to 0 HP or below. Injury effects are meant to be immediate – you don't wait a beat and
then notice that your arm is off or your brains are scrambled.
The offending passage is on p. B419:
"In addition to the above effects, make a HT roll at the start of your next turn, at -1 per full multiple of HP below zero."
which would be clearer as:
"In addition to the above effects, make an immediate HT roll, at -1 per full multiple of HP below zero."
The later text:
Success means you can act normally, but must roll again every turn to continue functioning.
would then be better as:
Success means you can act normally, but must roll again at the start of every turn to continue functioning.