I Tier Transplanted for 2 years before I changed to what I do now. Mostly because now I grow 99% feminized and there's no need to transplant. As Autos don't have that recovery time (veg like a Photoperiod) so any stunting you do is permanent. Me personally I always transplanted when they were wet because I didn't want to tear roots. However, with tiering you already have your starter cup pre cut and place in final pot. Now this ties into STB's last comment...
I also disagree. When I tiered autos I stareted in 32 oz cups or 44oz cups and then transplanted into 1 gallon grow bags. I don't know if you've ever seen any of my grows but I've had monsters in 1 gallons. Granted now that I grow in 2 gallons straight away I get bigger yields.... But unless you absolutely HAVE to have a big huge ass yield, or you have a personal thing against 1 gallons, you will be just fine leaving a potential female in a 1 gallon pot.
I've pulled 2.5-4.5 ounces off a 1 gallon auto and nearly 5 ounces off a photo once in a 1 gallon. You also have to consider genetics... Especially in autos... If you get a small pheno she's gonna be small and you can't do anything about that. As opposed to photos where you can veg her to the size of your liking and make her big. Just keep that in mind.
If it was me personally I'd leave her in the 1 gallon. But again if you have to transplant... do your best to not rip and tear the roots. You may want to water a bit along the sides and let it seep down to the bottom just to help that process and it's not so dry... IME most Autos don't skip a beat when transplanted. You may have a few day or even up to a week of "down time" but I've only experienced that a few times. And I've tiered 100's of plants. So I do have tons of experience doing it. If you get her too late where she's root bound and the roots are swirling around the botton of the pot she may not grow much more at all... So consider that as well...
Best of luck man!