I am not a lawyer.

I do have some old $n$th to default term sheets just laying around. Readnig them, I interpret their language to work very similarly to the cheapest-to-delver language in single-name CDS. To emphasize again this is just my understanding of some complex legalese and I could be missing something.

Recall that with the single-name CDS, after the credit event, the protection buyer can either physically deliver one of the obligations pari passu with the reference obligation; or pay cash amount determined at the auction. Natually, the protection buyer will choose whichever is the cheapest for him.

My interprettion of my old ntd term sheets is that if the $n$th and the $n+1$st credit events happen on the same day, then the protection buyer can either physically deliver one of the obligations pari passu with either the $n$th or the $n+1$st reference obligation; or pay cash amount determined at either $n$th or the $n+1$st auction. Again, we can expect the the protection buyer to choose the cheapest.

However, sorry, I'm not sure how this connects to default correlation.