It is totally up to you, but I suppose in a way they know they have booked a small place, and if they are comfortable with that, maybe it doesn't have to concern you? (Unless it does concern you, in which case you can be concerned since it is your property.)
I don't know that you are being lied to, it's just if people normally stay in hotels and then start using Airbnb, like if I book a room with two queen beds in a motel the front desk agent won't bat an eye if 14 people follow me to my room. If we are rowdy at 3am it's a different matter. I would never think to clarify when booking a hotel how many people are staying in my room, and especially who they are, the times they will arrive and depart, etc etc. Airbnb is obviously a different thing, but it is something people have to get used to - having someone pry into their intentions, schedule and guest list. You say your place accomodates 4 at most. Mom, dad and son are 3. Maybe the day auntie and uncle get there the cousins are going to move into the dorm and hang out for a few nights while mom, dad, uncle, and auntie crash as a group of 4 at your place. Maybe things have gone sideways somehow at the last minute and all of this is just some travel inconvenience last minute, as often happens with people traveling. I don't think you have to assume ill intentions or bad manners.
So you have some options I think as far as response.
You could completely let it slide and give humanity a chance to prove it's excellence to you.
You could do something like only provide towels and linens for the # of guests originally requested, then let them ask for additional linens and charge for that.
You could have a diplomatic pre-arrival conversation letting this young man know that he wasn't forthcoming with the details of his reservation and you are going to charge an additional fee per guest, so he should let you know how many guests will be there per night so you can charge accordingly...or however you want to do that. You could even suggest a flat fee rather than trying to figure it all out - an additional $100 or whatever it may be.
You could put them out on their nose the day before their arrival for a "Big Life Event" and be remembered as part of a tale of trial and inconvenience in their family lore.
