Urchins coordinate their reproduction via a few different signals, thought to be tides or lunar cycles. Once they decide it's time to have babies, they will release either eggs or sperm into the water, depending on if they're male or female. The eggs and sperm mix, the eggs are fertilized, and they drift away to land and hatch. Many corals and sessile (still) reef inverts practice a similar method, as it allows slow-moving animals to send their babies far away to new habitats.
I've heard a few stories of urchins successfully breeding in aquaria, but usually they either don't get the right signals or their eggs are just sucked up into the filtration. That, or fish just go nuts and eat all the eggs.
They don't mate via physical contact, they don't even have to be all that close to each other to reproduce. They're probably all hanging out in the same spot just because it's a good spot for urchins, not because they're trying to mate.
