I'm running it on Android version 6.0 and most of the time, the App remembers the last position correctly when turning off the phone (standby mode). But it has also happened many times that the App simply jumps to the beginning of the next chapter regardless of where you were in the (previous) chapter.
Since Android 6 is rather quick in terminating background applications to save memory and storage, I assume the App doesn't have the time to log the correct current position inside an e-Book before it is shut down by the operating system.
The bookmark function works and helps but it should be unnecessary if you just want to continue where you left off. Also, when calling up bookmarks it seems that you have to be in the corresponding chapter of the e-book for it to work.
Hope this feedback helps and I'm happy to provide more information if necessary!

Thanks,
Tale