Hacker Rank: Counting names with prefix matches using a trie
You don't validate your input.  If the user enters a string with no space in it, you'll get an exception.

s[0] is a character, so why do you convert it to a string to convert it back to a character?

You should avoid allocating _trieArray until you need it.  Otherwise you'll allocate a bunch of memory you don't use (in all your leaf nodes).

You don't need to use _findCount.  Your private find method can just return that value.

As an additional exercise, rewrite add to not be recursive, and avoid making all those (sub)string copies.