What you are doing at the back connector is reading voltages across a 1 ohm resistor on the cathodes of each pair of power tubes. Since it's 1 ohm the math works out to mV = mA, so in your case we can say your pair of tubes is drawing 15 mA. It's very low, but it won't hurt anything. A current draw of this low usually means the grid is seeing too much negative bias voltage. The higher the negative bias voltage applied, the colder the tube will run (draw less current). These boards usually conduct some of the positive plate voltage to the grid pin, causing it to go less negative and therefore conduct more. In some cases, a lot more until the tube dies or the board burns up.
I'd measure what the voltages are on pin 5 of the EL34s, and I'd also have a look at those 1 ohm resistors. Also, you didn't say if these are known good tubes or not, if they were in the amp when it blew up, they may just be pooched.