I can confirm the problem and the workaround concerning the japanese time zone. My LinkStation Duo didn't wake up at the scheduled time after a firmware upgrade to V1.37. As described above, the problem is that shutdown time is your set time zone but wakeup time is japanese time. I live in Germany (GMT+1), my settings were 07:00 AM wake up and 01:00 AM (=25:00) shutdown. After the upgrade, the NAS went to sleep at 01:00 AM but didn't come back at 07:00 AM.
When you consider the cause of the problem (Wake up time is japanese time, but shutdown time is set local time), it's all logical: The NAS shuts down at 01:00 AM local time. But as 07:00 AM wake up time is japanese time, that would be 11:00 PM GMT - when my NAS is still running. So the wake up order has no effect as the LinkStation is already working.
Workaround: Leave the settings for the shutdown but change the settings for wake up according to japanese time. My working settings for wake up at 07:00 AM and shutdown at 01:00 AM GMT+1 now are:
Wake up: 15:00
Shutdown: 25:00
By the way: The fact that it takes Buffalo months to patch such a simple bug (I just installed firmware v1.40 and the problem is still the same) made me think about buying a more expensive NAS next time.