The fact that your tree still shows up in indexing does not mean that it isn't yet private - that takes effect immediately, but the indexing could lag for several weeks. People will not be able to access the tree, but will know who is in it from the indexing.
I would not push a panic button, but if I were in your position, I would make the Facebook information unavailable except by invitation (or however Facebook handles such things - I'm not a member). There are some innocuous (although annoying) possible explanations that have nothing to do with identity theft or the like - but I would say, why put up with it if this is bothering you?
Some possible explanations - this is a clueless soul who thinks that if someone has the same name as a person they are seeking, it's in fact the same person. Or, maybe they made a wrong connection several generations back, and now are on a path that leads to your immediate family, in which case they might sincerely (but mistakenly) believe you are a relative. It could be a coincidence that you were contacted on Facebook, but might not be - again, if it bothers you to think there is something amiss, your decision to simply insulate yourself most likely is a good one. If nothing else, the person who has been copying things may contact you to find out more.
Good luck with this.