The stone surface is not what’s waterproof, the surface is a sacrificial wear layer. If the roof is leaking the underlying waterproofing has failed. You need to hire a qualified flat roofing specialist and discuss options for what works in your area and specific roof. That can mean rubber with a floating wood deck, tpo with tile on standoffs, welded copper, hydrostop with a decorative wear layer added.

We are just now going through a complete deck replacement, because the builder used stamped concrete as the surface. Leaked, cracked, flaked, just looked like crap. Found no pressure treated wood used for beams and joists, too. Putting a nice composite deck and a beautiful undercover system that is meant to be used with decks - it doesn’t touch the joists underneath and has gutters to divert all rain.

Yeah, it's what's under the stone that's the leak rather than the pretty topping being the issue. How is it leaking, where in the the porch ceiling, or other? I ask because though I don't know much about gutters, that looks like a lot of roof for the couple downspouts, plus the porch roof also feeds into those downspouts. Is all that draining out OK? You have some overflow happening off the porch roof, you can see the marks on the gutters. So there is an issue there. Considering the snow buildup, could you be getting some ice damming issues too?

Thanks @beesneeds. Yes, the leaks are on the porch ceiling. They are spotty. My guess was water leaked through some of the cracked tile joints and through the bad waterproofing underneath. The gutters themselves are working fine. But you are right about the overflow and the water marks on the siding. It is possible some overflow could have found its way back to under the tile. Thanks again!