There are a few possibilities:
1. Your cue isn't actually 3/8-10, and therefore the 3/8-10 shaft doesn't fit properly. I'm sure you know what pin your cue has, but I include this possibility because... well... it's possible.
2. Your cue is 3/8-10. The shaft you bought is mislabeled "3/8-10", but is actually a Radial shaft or some other threading.
3. The threaded hole in the shaft just isn't deep enough to accommodate your cue's pin.
If #1 or #2 are true, you need a shaft with the correct threading.
If #3 is true, a cuesmith should easily be able to bore and thread the shaft a little deeper.
Good luck!