Tube Fire What Next?

I have a melody el34 integrated amp. I truthfully don’t know much about how to maintain it. About a year ago I had a well respected tech do some work on it and put in new tubes. Last night the family was listening to music and it looked like there was fire inside of one of the power tubes. Scared the crap out of my daughter. I turned off the power and unplugged it.  I assume I need to replace the tube. Is there anything else I should do? I have never biased the amp myself but I did just buy a multimeter which ironically just came this week. Can someone walk me through this so I don’t bust my amp or more tubes. Thanks for the help. 
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Yes. Plugged in, turned on, and warmed up. 

For now while its missing a tube I would leave it unplugged. Unlike SS amps that don't care tube amps don't like to be on without being connected to a speaker. Its overkill, but just to be safe I turn off and unplug when changing tubes or speaker cables.  

When its warmed up half an hour or so the black neg lead goes in the center and the red goes to one side or the other. You want a really small screwdriver like for glasses. Do it right and the probes will hang in there leaving a hand free to turn the screw. That's my preferred technique as otherwise you're trying to hold two probes with one hand while twidding the screwdriver with the other which is a dexterity test I have passed but would rather cheat my way out of, if you get my drift.
Actually the tube arced. This usually happens when the tube has aged out, or has been damaged. The usual culprit is a sort of paint on the cathode of the tube, which can flake off, and it is conductive. This is the genesis of the arcing.

I would replace the tube and see how the amp behaves. In some amps, the arcing can cause resistors in the amp to be damaged, in which case the amp might not work correctly when the tube is replaced (it won't bias up, the tube might turn cherry red or it might sound distorted). If you can set the bias that's good; play it and see how it sounds. If that's OK, the amp is OK and you just need to be sure that your tubes are biased correctly.

This can happen even if the tubes were biased correctly, since its a function of the condition of the cathode coating and not really anything else (although if over-biased can lead to failure).
Atmosphere and millercarbon, thanks for walking me through this. Now I have a choice do I replace the 1 tubestore preferred series el 34 or try something new. Previously it was recommended to me that I try the Mesa boogie NOS el34 but at around $400 quad that’s above what I can afford. So if I go with the new quad route I am torn between trying out Gold lion kt77 for $150
or waiting for Germany to allow shipments to US and try the NOS Siemens for $220.