That Amazon page has plenty of reviews panning the power supply: "Power supply cannot handle 2A, let alone the 1.6A my 12V LED string requires. Goes into over-current mode at 1A.". Another review states that it has a 1.5A fuse inside.
There are much better options for driving steppers than a motor shield like the one you linked. "RAMPS" shields with drivers included should be available on Amazon or eBay, and then you can use any power supply 12V-40V, like an old laptop power supply, and get better performance from your stepper motors without the worry of overheating them.