If the voltage of the adapter matches the voltage of the device, the device will draw only as much current as it needs. The 1 Amp on the adapter is the maximum current that it can safely provide. However...if the adapter is not the "regulated" type, the voltage will be about 1.4 times higher than the specified output voltage with a light load or no load. With those types you want the current rating of the adapter to be close to the current requirement of the device.
Ken