I'm right there with Neil on this one. More likely uneven drying than fast drying. I have fast dried all sorts of clay bodies, both US commercial ones, as well as my own claybody formulations, and also ones from when working in Japan with numerous of their clay bodies....... and have not found warping to typically come from "fast" drying.
Or as was already mentioned, it could be from a ware board that is not actually flat (or one that changes shape when it absorbs moisture from the pot).
As a side note, one clay body I used while working in Japan would seriously self-destruct in about 5 minutes (massive...... and I mean massive.... cracking) if you put a close to leather-hard pot direcdtly into the sunshine to dry....... which is usually a great technique to use for so many clay bodies. Repeated testing of this with all manner of forms proved it completely.
Another body I used in Japan would self-destruct (cracking again) if you covered it with plastic overnight to retard drying. The slight condensation on the inside of the plastic hitting the clay surface got re-absorbed in localized areas... and "bingo"....gone!!!! Had to use layers of opened newspapers to place over the forms....... it retarded the drying and let the moisture slowly breathe through the paper's pores.
I rarely use bats, even for most dinner sized plates and small to medium bowls. (Big platters and something like a 24" diameter at the rim bowl... well yes.... bats are for sure used .) I just pick them up off the wheelhead. And I throw a lot of smaller things off the hump and pick them off "spinning". If I chose the pieces to be "round" there does not seem to be an issue from the "wet handling". If they are slightly off round, a tiny pat or two at the correct time (not when fresh thrown) takes care of that.
And frequently those fresh thrown forms head right out of the studio door and into the graveled kiln yard and into the sun and wind to start to dry for eventual trimming or finishing. When they are trimmed/finished, they also then often go back outside into the wind/sun to dry from leatherhard to bone dry...... before the bisque (although many are stacked in the wood lkiln yakishime... and do not get bisqued). Good clay bodies.
A lot of times the issues are claybody issues too....... and not how YOU are handling the pieces. Just because a clay body comes from a "supplier" does not mean it is necessarily a GOOD claybody and the supplier actually has a strong technical background in clay body development. In this country (USA), to be a "ceramic materials supplier company" does not require any certifications or specific training.... just a "shingle" hanging outside the door. I've tried some commercial bodies that are not all that great.
Please post pictures, what does this warping look like?
At the pottery in Japan where I spent some time, distortion through the throwing,drying and firing was appreciated.