The auto-age settings are only for Sims and Pets/Horses to my knowledge.
Did you create them as adult animals ? Not sure how fast they age on normal age span (or if that even affects the farm animals) but since you created them all at the same time, it makes sense that they die together.
I don't think there's a setting to have them not age while you don't play them but I'm totally unsure on the intention here.
Maxis will need to decide if there's a bug here or not.
This may have been an oversight in their design then.
The cow, llama and chickens etc simply spawned after purchasing them from the barn/coop as adults. Just the normal means of obtaining them. Hopefully Maxis will consider extending the coding to the other animals then. It's just silly not to really 🤔
Thanks for addressing this - and hopefully eventually this will be landing on the laundry list.
