At what point during an organism’s lifespan do mutations occur?
I'm assuming this question is primarily interested in heritable mutations, given the evolutionary nature of the link you shared. Only mutations in germ cells are heritable, so it will vary between males and females.
Female germ cells are formed in utero. Oogenesis in humans and is pretty much finished by 20 weeks gestational age (there's some debate about this, but it seems to be the current consensus view). So any heritable mutations would need to happen during gestational period. Note that that gestational age number probably varies quite a bit for different animals, but I think it's generally completed before gestation is completed (in mammals at least).
Males produce gametes via spermatogenesis continuously throughout life. So, for modeling purposes, you could probably use the age at which they conceive (though the sperm actually take a couple of months to mature).
One thing I'm unsure about is whether or not aging in the male affects the mutation rates in sperm, but might be something for the OP to look into.