The reason that tuners go on with the tuning key away from the nut is because the string tension then pulls the gear at the end of the tuning post against the gear on the tuning key spindle and keeps everything as tight as it can be. Fitting the tuners in the reverse manner and the tension pulls the gears apart.
New tuners will feel and work fine, but as they age and wear, the tuners will become sloppier and far less precise, with more backlash. And the fact that the gears are loose will allow more vibration, which in turn will provoke more wear.
So you might want to think about turning them round if you think the guitar’s a keeper.
Nice work on the two guitars though.