Hi Nikolay,
I have reproduced and found this bug. It's simply that the pedestal values are not being written to the file cache.
The workaround when you have to use pedestal values is, as you've discovered, disabling the file cache in ImageIntegration. Users that don't need pedestals are unaffected by this bug and hence don't have to care.
I'll try to release a new version of the ImageIntegration module as soon as possible, with this bug fixed of course. The next version will also include the new HDRComposition tool, which I'm writing right now.
Thank you for your bug report, and sorry for forcing you to disable II's file cache...