Only Spartans can be Spartan Hoplites. No one else could. It required specialized training. The Lakedemonians didn't go around colonizing and then sending people there to live forever. They were all based in Sparta. Everyone else was a slave to them.

So in conclusion YES, Spartans Hoplites SHOULD only be made in Sparta. But i guess Syracuse could import them. I guess it makes sense like that.