It will happen, and how you handle the first hour matters more than what actually went wrong.
Start by separating two things that feel identical when a patient is upset in front of you. Is this a complication, meaning something clinical has gone wrong and needs treating? Or is this dissatisfaction, meaning the result is clinically fine and not what they wanted? They need completely different responses and confusing them makes both worse.
For a complication, act first and discuss second. Assess, treat, escalate if you need to, and document as you go. The conversation matters but the tissue does not wait.
For dissatisfaction, the opposite. Do not reach for a syringe. The instinct to fix it immediately with more product is strong and usually wrong, because you are treating your own discomfort rather than their face. Look properly, compare against the baseline photographs you took, and establish what specifically they are unhappy with.
Sometimes the honest answer is that it is settling and needs two more weeks. Sometimes it is asymmetric and you can improve it. Sometimes they wanted something the treatment was never going to deliver, which is a consultation failure rather than a technical one, and worth recognising as such so you do not repeat it.
On the conversation itself, a few things consistently help. Let them finish. People who are interrupted while complaining escalate. Acknowledge the specific thing rather than offering a general apology, because a general apology reads as a formula. Say what you can and cannot do, plainly. And give them a timeframe, because uncertainty is what turns irritation into a complaint.
Avoid two phrases in particular. Do not say this is normal without explaining why, because it sounds dismissive. And do not say you should have known, because it puts the consultation failure on them.
Refunds are a business decision rather than a clinical one, and there is no universal right answer. What is worth avoiding is the reflexive refund offered to make an uncomfortable conversation stop, because it often reads as an admission and rarely satisfies anyone who is genuinely upset about their face.
Document everything, the same day, in the patient's own words where you can. What they said, what you observed, what you offered, what you agreed. If this ever becomes a formal complaint, contemporaneous notes written before you knew there would be a complaint are worth far more than a reconstruction.
Tell your insurer earlier than feels necessary. Policies usually require notification of circumstances that might give rise to a claim, not just of actual claims, and late notification is a common reason cover gets disputed. A quick call costs you nothing.
The last thing, and the one people find hardest: some patients will leave unhappy however well you handle it. You can control the standard of your work and the honesty of your response. You cannot guarantee the outcome of someone else's feelings about their appearance, and treating that as a failure will burn you out inside two years.