Hi there, welcome to BYC!
Please remove the pepper from the water and don't be so fast to jump on those type of suggestions. I would be using plain water or water with poultry nutri drench to support their immune system in a way that really adds up. No supplement should be given more than 10 days in a row.
What are you feeding? Is it a formulated turkey or game bird starter ration? This will be key to all things health related.
Maybe you just pushed on the crop to hard and stuff came out?? Was the vomit just liquid or was there stuff in it?
When it's hot like that... excess water consumption may play into droppings conditions.
In order to help a "sick" turkey... or any animal, it's really best to identify what you are intending to treat instead of throwing unknown fixes that might make symptoms worse or mask or alter them.
The pullet did not likely make the turkeys sick that fast. However it's good to be aware if black head is a problem in your area. It is a condition in turkeys caused by being kept with chickens... when a certain parasitic worm is present in chicken droppings. Getting a fecal float done a few times per year and see where YOUR parasite load stands is a great tool. Treating with the correct med if needed, works well. Many folks will swear certain symptoms (like muddy bum or yellow or foamy poo) are worms, but my fecal floats say that's not necessarily true. Testing will tell a better story. Black head isn't a problem in my area. Contact your local agriculture department and ask them or talk with other keepers of both species in your area. Adding your general location to your profile can help peeps make the most relevant suggestions possible.
Turkeys can be quite a blast, fun creatures!