It looks to me like Colors > Auto-Adjust Colors isn't available for batch operations in FastStone.
And you can't do it just by selecting a bunch of images directly from a folder either. Browsing an image folder, I tried applying auto-adjust to three images (select 3 images, then go Colors > Auto-Adjust Colors). The result was horrible. FastStone seemed to average out the colours from all three images and apply that to the auto-adjust result. And it only seemed to work on the last image in the series too.
For what it's worth, other freeware image viewers/editors I like (eg
IrfanView and
XnView) do offer colour auto-adjust as a batch operation, if that is important to you.