Can we install our glass and stone back splash right away after granite counter top installation or do we need to wait 12 or 24 hours for granite to cure?

don't worry, go ahead and install it. The granits been curing for thousands of years

The granite itself doesn't "cure", but the epoxy used to install any undermount sinks will typically take a day or two to cure.

Still, as long as you're careful not to jar the sink, I don't see a problem with installing your backsplash as the epoxy is curing.

I don't think you need to let it cure and while the epoxy is curing you have no problem installing your back splash