Who said they are really your mother and sister?
Well, It's really seems to me that Jo and Flora are the mother and sister of the MC.
He may be a bit confused by is back in past travel, but the two talk like they are his family...
Maybe the MC is a foster kid, so they aren't his biologic family. But I haven't found any clues yet that confirm this.
If this is indeed the case, I think it's will be great to have some info about it.
This would add some depth to the history and psychology of the MC.
Maybe it's just cliché and some "cheap psychology", but having been abandoned by his biological parents may explain a bit the lack of confidence and low self-esteem the MC has.