If you check this documentary, you'll see that Borneo natives used blow pipes vs Japanese during 1944-1945. I find this sort of engagement fascinating, since the poison used in the blowpipe dart must have been fast-acting to prevent retaliation by a firearm-wielding soldier. What accounts/sources exist about these skirmishes? What kind of poison was used? What were the outcomes of the skirmishes?
Google's first response provides an answer, that describes the likely toxin. The paper mentions that, "Animals hit by a poison dart, irrespective of the part of the body that is pierced, start to twitch after a few seconds." and, "Reports on dosage specify that 0.3 mg would be lethal for a rabbit. One mg. causes death in dogs (Boer et al. 1999:127), while 0.1mg. is the lethal dosage (L50) per kg. weight for cats (Zahorka 1986:58). The toxicity of [beta]-Antiarin is much higher than that of curare."
I am not a pharmacologist, nor do I play one on the internet. I haven't seen the documentary. With those caveats out of the way.
"Start to twitch after a few seconds" implies that there are (at least) two different models of the blowpipe as a weapon. "a few seconds" is ample time to fire a weapon, if you are aware that you have been attacked. I think it is more likely that the blowpipe wielders were acting from stealth and that the victims were unaware that they had been attacked.
It may be that the victim thought they were attacked by an insect, and were unaware of an attacker; they therefore did not retaliate until the toxic effects had started.
It may be that the victim knew that he had been attacked, but couldn't find the (stealthed) attacker. (I'm also not infantry, but my understanding is that spraying 360 degrees with an automatic weapon is, at a minimum, foolish and wasteful.)
I would like someone to explain why the toxicity for rabbits and dogs is measured as an absolute, while the toxicity for cats is in mg/kg. Which is a better model for humans? Is it possible to deliver 3mg to a human via a blowpipe?