Chemical process behind hardening ice cream
I don't think there's a chemical process here. It just takes a really long time for it to freeze solid. After 5-6 hours it was probably firmer around the outside than in the middle, and after a day it was probably fully frozen. (I've made a lot of ice cream, and have reliably seen this.)

It takes so long because the heat transfer is so inefficient. It's already bad since there's no convection, just slow conduction from the outside in. And the conduction is slow because your ice cream is basically insulating itself: it's full of air.

If there is something on top of that, it's probably that your emulsion is breaking as it freezes, so water gets forced out and freezes into harder ice. This would be pretty noticeable - you'd get a grainy, icy texture. (If you really are mixing whipped cream and nutella I can certainly see that happening.)