Yes, 100% sure, forget the mA scale, use a DC volts scale. Your meter may have a DC mV scale, set it to at least 50 mV to read the bias. And you are correct, at close to 400 Plate volts, and 40 mA of current through one tube, that is approx 16 watts. Typically, look for the tubes' Plates to glow red if biased too hot. Likely no damage to your amp, but there could be damage if you run it with the bias too hot, and 40 mV is too hot. Depending on how long you have used the amp like this, the tubes may have been damaged if the Plates were red.
The probe uses a 1 ohm resistor in series with the tube Cathode. There is a current running through the resistor when the tube is conducting. Using Ohms Law, we know that the current running through a resistor results in a voltage drop across the resistor. The voltage drop is what you are measuring with the probe. When a 1 ohm resistor is used, the mV reading translates directly to mA. Although you are reading mV, it is the same number when converted to mA using Ohm's Law. If this seems difficult for you to understand, do some research on Ohm's law to gain some knowledge about the relationship of resistance, current and voltage. Understanding the electronic principles involved in this testing method aren't nearly as important as following the directions for the equipment that you are using.