I am not a lawyer.
I do have some old $n$th to default term sheets just layinglying around. ReadnigReading 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 well 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 interprettioninterpretation of my old ntdthe 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. The protection buyer chooses which event to serve notice on, and which physical defaulted obligation, or cash to deliver.
IfFurther, if only the $n$th event occurs, then the protection buyer can still 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 thinksee that the buyer is obligated to serve notice on the $n$th event and is not allowed to wait for a more favorable 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 do, then you'd still collect on the defaulted quasi of your choice (paying premium until the day of the event you choose to serve notice for).