I know this is an old thread, but in case this helps others I did the following check this evening, under Win 10 (but I believe that it is equally valid under Win 7 and 8 too).
In short: Reflect will wake a PC from Hibernate or Sleep provided you enable Wake Timers on Advanced Power settings
Using Control Panel->Power options, I reset the current plan to MS default settings.
I then checked the Sleep settings Everything was set to Sleep, with Hibernate activated after 180 mins of sleep
I'm happy to accept this.
I then checked the Allow Wake Timers
setting; On Battery Disabled; On Mains Power was set to Important Wake Timers Only
I googled to find a Tenforums article
describing this (new) Win 10 feature. I read it to mean that only MS Windows services currently qualify as "important". THEREFORE I changed the On Mains wake Timer to Enable
and saved Power Options changes.
Next I started Macrium Reflect and scheduled an Incremental Backup to run once only in 10 minutes time; and closed Reflect.
I immediately Hibernated the machine, leaving it plugged in because that is a condition of my scheduled job.
Ten minutes later, the laptop fired up, ran the backup and re-hibernated (as set in Reflect Power Saving options), all just as it says in the manual
Hope this clears any doubts readers may have.