I hate to say this, but you may have a head gasket issue. This happened to me on my 91. Either the heads are lifting and allowing blow-by gas into the coolant (like my car), or the gasket has failed. In either case, this will flash boil the coolant and create steam voids that will propagate to the coolant tank, causing the blowout. Doubtful it is the thermostat because they usually fail open, not closed. I would buy a combustion gas test kit and test it on the coolant bottle. It's cheap, but will definitely confirm a blown head gasket or not. If not, you're boiling coolant somehow. The NSX can blow coolant out of the overflow tube, but only after several hard laps in hot weather where the stock cooling system cannot keep up. A 15 min drive around town is not enough to cause this behavior on a fully functional cooling system.