Scenario:
I have an unwanted dude at an opposing private deed who accepts a callout while I have an Alice Stow somewhere on the table.
Questions:
Can Alice Stow join the posse as the dude becomes wanted upon accepting?
When does Alice actually join the posse? Is it during making posses or when the callout is accepted?
Thanks
If one of your wanted dudes accepts a call-out, Alice may join the posse from any location (without booting, and even while booted).
Alice can’t join using her trait if your dude wasn’t already wanted as your wanted dude didn’t accept a call-out.
Alice joins your posse in the usual posse forming step, she can just ignore the usual distance and booting requirements.
Someone from the rules team will probably drop by to scold me for answering this momentarily.
RT is examining this process to be sure.
Kudos to @forkbanger, you’ve got the right of it 
Alice’s trait says: If one of your wanted dudes accepts a call-out, Alice may join the posse from any location (without booting, and even while booted).
So the key thing here is if a wanted dude accepted the call-out. In this scenario it comes down to when does a dude gain bounty for a shootout at a private location controlled by the opponent? This is clarified in the FAQ under Bounty:
After posses are formed, if the location of a shootout is at a Private location (homes are always considered Private), all dudes not owned by the deed’s owner get 1 bounty.
So since the bounty isn’t gained until after the posse has formed, your dude does not gain that bounty until after you form your posse. So Alice’s trait does not trigger.
To your other question… supposing the dude was already wanted. Alice’s trait is relevant when it comes to when you form your posse, during the forming posses stage.