This traverses the whole tree, and every time there's a match, pushes the current node to this array.

This sounds like a case for having the array as a property of the Tree object as it is a property which relates directly to the object. At the very least you could use a lexical over package variable as it isn't needed in your case.

But I have a feeling I'm breaking some fundamental OO rules, or maybe this is an example of a ghastly global variable?

I think if you're just writing a small program then it's alright to have somewhat messy OO as long as you're sure it's just a throwaway script. Much like using strict it's a good habit to get into applying proper OO structure to your programs consistently so that your skill remains honed and you're less likely to slip up in future.
HTH

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broquaint