Whilst I am sure that most/all of the standard consumer 'energy monitors' do not bother to attempt to determine direction of energy flow, as recently discussed, I don't think the fact that a monitor has no wired connection to the mains precludes the possibility of doing that - the voltage waveform can probably be sensed by capacitive coupling.The owl being battery operated cannot obtain any indication of the phase of the voltage so cannot determine the direction of energy flow. They obviously assume energy will only flow from meter to consumer unit.
Don't forget that, in the context we're talking about, precise determination of the current/voltage phase difference is not required. Depending on the direction of energy flow it will either be 'around zero' or 'around 180°'.
Kind Regards, John