Learn French: L'horloger doit régler le mécanisme avant que le client arrive. - The watchmaker must regulate the mechanism before the customer arrives.

Because the phrase avant que (before) is a strict trigger for the subjunctive mood. In French, you cannot use the future tense after avant que, even if the event hasn't happened yet. You must use the present subjunctive.

Is arrive actually in the subjunctive here? It looks identical to the normal present tense.

Yes, it is the present subjunctive! For all regular -er verbs like arriver, the il/elle/on conjugations are exactly the same in both the present indicative and the present subjunctive. We know it is the subjunctive structurally because it directly follows avant que.

I sometimes see an extra ne after avant que. Could we say avant que le client n'arrive?

Yes, you could. That is called the ne explétif, which is a formal, untranslated ne that sometimes follows avant que. It is completely optional, and dropping it as this sentence does is very common in modern, everyday French.

How could we apply the current lesson's focus (non seulement... mais aussi) to this sentence to emphasize that both the action and the timing are strict requirements?

You could say L'horloger doit non seulement régler le mécanisme, mais aussi le faire avant que le client arrive (The watchmaker must not only regulate the mechanism, but also do it before the customer arrives). This uses the correlative conjunctions to split the emphasis perfectly between the required task and the deadline.