There are several things that your tech can check out.
Changing the tone controls is not increasing the hum. This is just revealing what is already there. Not using a variac to power up a new capacitor should not be an issue. They never did this when they were manufacturing the amps. It is a good idea, but not necessary.
Look at the recap that the first tech performed.
1) An insulator must be installed between the chassis and the can capacitor (C17) or there will be hum. Make sure that they didn't ground the can to the chassis with a wire. The cap can ground return should be only be connected to the ground bus.
2) Check all the solder joints in the power supply and ground bus. Reflow them. A bad solder joint can cause noise in the power supply.
3) Check the main ground point for the amp at the end of the ground buss at the input jack. Make sure there is a clean contact to the chassis and that the connection is tight. Clean the jack contacts, including the ground shunt, with deoxit.
4) Hum pots can be a problem. It is hard to tell from the video but when they are blown, the hum is usually louder. You can disconnect the pot and test it with an ohm meter. An alternate solution would be to disconnect the pot and replace it in the heater circuit with two 100 ohm 1/2 watt resistors.
5) Plug an instrument cable into the ext amp jack and plug into the input of another amp. If it is hum free, this tells you that the problem is not in the preamp.
6) Remove the pre-amp tubes from one channel at a time and check the amp for hum. This can help identify a problem in specific locations. In general, a bad tube can have different symptoms. Swap out all the tubes.
7) Twisting the heater wires whenever possible helps reduce hum.
8) A scope or a signal tracer can help identify the source of the noise. Use these after the more obvious possibilities have been eliminated.
9) In some cases, the design of the amp is the cause of hum. The V4 hums. The power supply can be made quieter by increasing the value of the capacitors. For example, C17 can be increased from 40 to 100uF. The main capacitor, parallel 100uF and 40uF in series with to 100uF (=58uF) can be increased with two series 220uF caps (=110uF). Depending on the amp, you have to make sure that the board will fit. I use
SDS Labs Dynaco MK3 upgrade capacitor boards, available from Triode Electronics in amps for this. I use high current capacity Panasonic snap-in EETEE2G221KJ (220uF 400V, EE series) that are available from Newark. See post 87
SVT recap for an example. The SVT and the V4 use the same first cap configuration. This is a major overhaul but, in my opinion, makes quite a difference. The cap values can be boosted to improve the amps performance without going to the extent of using a cap board. That's just my approach.