'non-mysteriously' is formed by the prefix 'non-' (from Old English/Latin use of 'non' meaning 'not') attached to 'mysteriously', where 'mysterious' ultimately comes via Latin from Greek 'mysterion' meaning 'secret'.

'mysterious' entered English from Old French (e.g. 'mysterieux') and Latin 'mysteriosus', which in turn came from Greek 'mysterion'; the adverbial suffix '-ly' produced 'mysteriously', and the negative prefix 'non-' was later attached to make 'non-mysteriously'.

Initially related to 'secret rites' or 'things kept secret' (from Greek 'mysterion'), the sense shifted to 'difficult to understand or explain'; 'non-mysteriously' now means 'in a way that is not secret or puzzling, plainly'.