Tube Tester

You CAN do that if you do it properly. To be certain that no damage will occur, unplug the amplifier before swapping tubes.  I don't know exactly what went wrong in your case, but maybe you swapped tubes with power on. Or if you turned the amplifier off via its power switch, perhaps that amplifier had a power supply that was always powered up, even when the switch was in the off position.  That is not uncommon but is usually done so not to be a danger.  In any case, if you pull the plug, you are safe.

Like I said, most vintage testers cannot deliver either enough plate voltage or plate current or both to properly test power tubes, and also a few high transconductance 9 pin miniature small signal tubes. So you will get a result but it may not represent what the tube actually does in your circuit. Ergo, it may be better to test a power tube in the amplifier circuit. There are exceptions of course. As tubes age, the grid bias voltage, which must be negative with respect to the cathode, drifts “up” from negative toward zero in order to pass the desired current. That’s “transcenductance”. So tubes that are trending toward zero difference from the cathode V over time are wearing out. That’s how tubes die.

What Dave said. Also, it’s “Amplitrex”, not Amplitron.

If you must buy a tube tester first learn about the features and capabilities of all the various Hickok testers. Then buy the best you can afford that has been refurbished, calibrated, and guaranteed by the seller. And keep in mind that most cannot properly test a power tube. For small signal tubes, they’re fine. I stipulate Hickok because they were the premier company and are still revered. Hence there are guys who can repair them, and parts are available. Also, they were simply the best. So far as I can tell, Hickok made the BK testers too. That’s if you’re going to buy vintage. If you want to spend big bucks and buy new, see Amplitron and others.

Agree with Viridian that you want a tester that measures transconductance. And that usually means Hickok or B&K (often made by Hickok.) Transconductance of a given tube varies with plate voltage and current. Unfortunately very few vintage testers are capable of providing adequate voltage and current for power tubes. Hence you may get a misleading reading for transconductance. Best to test power tubes in the amplifier where you can know plate V and current by direct calculation. And measure grid bias as a guide to tube wear. For big bucks you can get a modern tester that does a proper job, but IMO it’s not needed.

Budget?