The current rating of any power supply, or voltage regulator, is the maximum current it can provide. A device connected to that power supply will only take as much current from the supply as it requires. If it tries to take more than the supply can provide you risk breaking the supply, or the voltage "drooping" to a level that causes the device to stop working properly.
A constant-voltage supply never forces current.
You can think of it as a well, with the device being a bucket. You can't put a bucket down the well that's bigger than the well opening, and you will only draw as much water as will fit in your bucket. The well doesn't squirt water out at you.