Once you get a new spindle you will have to seat it properly again. VPI recommends using their 2-piece clamp for this - just screw it down tight and all should be OK, but maybe not.
After doing this ofiginally I saw a slight wobble on the platter bottom edge when it was spinning. VPI then said to remove the center spindle again, turn the platter 1/4 way round and reseat it again. After doing this twice everything was stable with no wobble. I guess the machining isn't always perfect but a little adjustment and all is well.
Enjoy,
Bob