"Das Mädchen kommt noch hinzu."
There are two different senses of "hinzukommen". 1) "to add to" - In this sense the phrase would mean: "(We have so much trouble already, and) the girl adds to it (to the mess)." No gender bias intended.
2) "to join"
(2) makes more sense in this context. But - The audio was "das Mädchen kommt NOCH hinzu." The accent on "noch" lets you rather think of meaning (1).
As to the (grammatically) present tense, for meaning (2) the "noch" tells us that she hasn't joined yet. "Das Mädchen kommt hinzu." is also correct German and just plain present tense. "The girl is joining."/"The girl joins."
So you are right interpreting the given sentence as taking place in the future.
In English, we generally use "going to" or "will" to express anything that hasn't happened yet, even if we're just about to do it ("I"m going to brush my teeth, and then we'll split." In German, you can express things in the near future by using the present tense, even when they haven't happened yet ("Ich putze mir die Zähne, dann hauen wir ab.") Native English speakers sometimes over-use werden+infinitive for the future in German (when they could just use the present tense), because they're translating what they'd say in English.
Here's an example that does work in English: "Tomorrow I fly to New York." (Morgen fliege ich nach New York.)
I think it's all context. In other words, the sentence probably means future, because it's talking about the girl joining (hence not yet joined). But, as with a lot of sentences, the same utterance can express future or present, depending on context. If you answer "Ich kaufe mir neue Schuhe." to the question "Was machst du heute?", and we're at a cafe, then that's the present expressing the future (something you'll do later today). If I meet you in the store, and we have the identical exchange, "Ich kaufe mir neue Schuhe." could be expressing what you're doing right then, in the present.
SO, I can imagine a situation where "Das Mädchen kommt noch hinzu." is describing the girl joining (the group) as we speak, right this moment (she just showed up). But it's more likely to be the future.
This is not a sentence where the English translation is a clear, obvious equivalent, but rather one possible equivalent.
Thanks. Only, I'm wondering how you would distinguish future tense expressed as present tense. Generally (I think) there's a flag in English--for example, you said "Tomorrow I fly to New York." In the sentence at issue, how do we know the Mädchen WILL join, but is not doing so now?