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 similtaneously, 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.

If the $n$th event occurs, then the protection buyer can choose to wait for the $n+1$st (or $n+2$nd etc) event to occur, and then serve notice on the protection seller for the $n+1$st event (or $n+2$nd etc). I don't think the buyer is obligated to serve notice on the $n$th event.

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

Suppose, as an extreme example, that you buy first to default ptotection on UMS sovereign and PEMEX and CFELEC (quasi's). Suppose than one of the quasis defaults Monday and another quasi defaults Wednesday, and finally the sovereign defaults Friday. You'd choose which notice to deliver based on your belief who has lower recovery, which would probably be one of the quasis. But if the sovereign never defaults, only the quasis you'd still collect on the defaulted quasi(s).