There is plenty of room for confusion here. We have both Cole and Coles as surnames, and we have single folk and married people (Cole/Coles and Coles/Coleses) and that's even before we add apostrophes.
No wonder people get confused!
Mr Cole's dinner party. The dinner party of Mr Cole.
Mr Coles' dinner party. The dinner party of Mr Coles.
Mr Coles's dinner party. The dinner party of Mr Coles again.
For Mr Coles it's a matter of style and preference which form you choose (Coles' / Coles's)
Back to Mr Cole.
Mr and Mrs Cole's dinner party. The dinner party of Mr and Mrs Cole.
So far, so good. But we're about to hit a problem - The Coles.
If we refer to Mr and Mrs Cole as The COLES...which we often do - we now have the dinner party of the COLES. The Coles' dinner party. Or, as we can choose the other style, The Coles's dinner party. They both boil down to The dinner party of the Coles. It will be the same pronunciation as The Coleses' dinner party - which itself has the alternative of the Coleses's dinner party, I suppose... but isn't that awful!
I think we all have to choose our own style, and then stick to it. I think the American teacher you contacted is correct, some Americans will choose one style, some the other. I am English, and I still am never sure which style I prefer, even after 60-odd years of speaking English.
There is no law about this. It is a matter of convention, style, and preference.
The problem here, I believe, is that we have Mr and Mrs COLE (surname Cole) being called The COLES which is very similar to Mr and Mrs COLES (surname Coles).
I'm going to post this now... and I'll read it again to see if it makes sense.
Apologies if it does not.
I'll ask the Apostrophe Protection Society.