You said that you switched to the snap in right?
The snap in have a checkball in the fitting, the screw in type have the checkball in the valve body. Having two checkballs isn't an issue. But not having one might be. Not sure that it would be an issue while running though.
Where under the car was the puddle? Driverside, passengerside, under radiator/engine/trans area?
Seems like you lost the fluid, where is the question that is likely the issue. If it popped out the vent on top of the trans, that's likely a channel plate gasket issue. An axle seal is easy enough to check/fix. Cooler line is also easy to fix.
