As far as I know they are not immune to venom from other spiders or from the same species or genus.
But
Puncher wounds kills just as fast as venom would, most of the time, I would think that a puncture wound from a female or male for that matter, will be fatal if bitten on the major "body" sections of the spider. Carapace and abdomen would be the 2 main body parts.
Might be a bit late, but, one needs to keep your spider hydrated with the amount of leakage that happened.
I don't think there has been much research on the subject of spiders being immune to there "own" venom?!