Yes, they should align correctly, but as Marcros says it is not too important for spindle turning. If you were doing copy turning with a tool held in a machine, then it would matter as it would turn a taper not a cylinder. But for hand held tools, you adjust automatically to wherever the axis lies.
The sort of time you would get into trouble would be if you held the work on the headstock and turned an indentation, then tried to put the tailstock centre into the indentation. But more commonly, you would out the indentation in with the tailstock, or else have it indented before mounting the work.
The only time you would notice is if you make a piece, then use a drill in the tailstock to put in a central hole. A big drill will be so stiff that it will still drill OK but make a hole bigger than the nominal size. A small drill will be flexed by the workpiece having a different centre, and might break.
I am not familiar with the Luna, but looking at the pictures it seems a good design and should not be that much out if assembled correctly. I suggest taking it to bits and reassembling, making sure the slides are all seated properly and (see above) that the centres are seated correctly. It does not look as if it has an adjustment for that alignment, but I don't have a manual to hand.
Keith