I have to admit, I don't play classical.

My best guess would be that the strings will settle down in a few days - much like steel strings do.

It could be that the new set is a slightly smaller gauge of string, or that the nut slot is a little too deep - thus causing the rattle.

The Nylon strings need to stretch out so you will be retuning for a few weeks. The next time you change strings, just change the wound strings.

As for the rattling, is it buzzing against one of the frets or at the nut?

yeah new nylon stings take forever to stay in tune .

I've had the rattling before when the knot at the bridge is kinda sitting weird and vibrating through the end . give it a yank it should stop

It could be that the excess string near the bridge is vibrating against the body when you play. If you haven't done so already, try cutting the excess strings a bit shorter so that they don't touch the body. Also make sure that the excess strings are cut short at the headstock too.