Supposedly means "in a way-assumed to be true or presumed as real or genuine." That is, what is supposedly a certain situation may not be a correct or accurate assumption: "He is supposedly in love with Helen, but this attachment seems to be only a rumor." Presumably means "probably," "reasonably," "capable of being taken for granted": "Since he is an expert, presumably he knows what he's talking about." What is presumably a truth is a probable or likely truth; what is supposedly a truth is a doubtful, questionable, suspicious, or undecided truth.
Dictionary of problem words and expressions. Harry Shaw. 1975.