Whether to link stockpiles or not is a matter of play style.
In your case it sounds you want your mason to realize he should haul stone to the stockpile and then draw from it, but that's not how it works. Hauling stones to stockpiles is a hauling job that's separate from the mason one (hauling a stone to the mason's workshop from either a stockpile or wherever they happen to be is a mason job, however).
If you link the stone stockpile to the mason's workshop it IS out of stone when the stockpile is empty, and the mason takes some other available job (which MIGHT be to haul a stone to the stockpile, but probably something else). If you've got loads of haulers that ensure the stockpile is stocked, linking is great, but if you're short of haulers that can cause production to stall whenever the haulers fail to keep up with demands.
If you don't link the stockpile to the workshop the mason MIGHT get the next stone to process from the stockpile, but he can just as well haul a recently dug stone from across the map. The production rate is lower, but the risk of production stalling is rather small (for stone; wood hauled from outside would stall immediately when you apply a civilian alert to keep your civvies from running out into the goblin siege).
But if I don't link the stockpile, and just use it to have a "close source" of stone shouldn't they still go self-gather stone if haulers are not able to keep pace? Or should I not set up stockpiles like this until after a migrant wave or two. And in the early going everyone has to haul (with exception of miner's maybe). I do disable hauling on my core craftsmen after I get some migrants to replace them.