I let mine out and she dose fine! She dose not go far, she just flies from the loft to the roof of my house and back . they are pretty good at spotting hawks. My birds won't fly if their is a hawk around.
reguardless of the info above, fantails are show birds and will be at a disadvantage out in the open, they are safer in an aviary, you make your own mind up as these are your birds, but I would be remiss if I did not at least warn you. you do have birds of prey in CA in fact you have 18 different ones, and as far as cats and dogs go, never saw a cat on my property for 4 years, untill I got pigeons, he had to be trapped and taken to the humane soc. so just because you don't see them know, the pigeons will attract preditors of all kinds and these fantails would be sitting ducks, esp with hawks. here are the 18 types of birds of prey you have in Ca.
I lost a really nice Indian Fantail cock to a cat or raccoon or some kind of predator besides a raptor just a few weeks ago, it sucks now I need to find a cock for my 3 hens... It was probably a cat they kill birds and other animals just for fun they often don't even eat them, a raptor or raccoon would've eaten him which is why I'm against outdoor cats.
Osprey, kites, kestrels, and eagles won't give you much problem. Your main concerns are the Cooper's Hawk (aka chicken hawk), Sharp-sins, Peregrines, and Merlin (aka pigeon hawk).
I would not let out American Fantails at all. Indian, Syrian, and Garden Fantails are much better fliers, but none are completely safe from hawks. They aren't very fast and make easy food for them. Cats and dogs can very easily snatch up American Fantails. If you let them out, do not leave the area unless you want your birds gone.
And by the way, it only takes a week to settle fantails.