I think the TSC setup seems to be showing what it should - mostly! I don't know how much of this you already know and understand but just in case... The Power Soak circuitry works by adding in a resistor chain which is designed so the amp output sees a constant impedance no matter what level is chosen. The resistor values are chosen so they drop a precise amount of the output power as heat leaving the reduced amount to feed to the speakers. That's easy stuff to understand but there is another bit which people sometimes miss. The first level of drop, from 40W to 20W, is done by pulling two of the output valves out of circuit. That is why you see the two inner LEDs kick in for all of the selections other than full 40W. They are indicating that those two valves, the inner pair, have been turned off by the control circuitry.
I think that the fact that sometimes at turn on you get an initial flash for some settings and sometimes you don't is not really relevant. The TSC seems to be ending up where it should for each setting. That "mostly" at the beginning was only there because of the 40W "left lights out then all lights out". If this is just a second or two then it's no problem, if it is a longer time then it could be significant.
The TSC is a feedback system and all such circuits have a settling time. It isn't surprising, taking into account the fact that this is a dynamic control of a static situation (the bias current), that that settling time should involve voltages taking a few seconds to reach their correct level when the system starts from cold. Each valve is controlled individually by a totally separate path to allow each one to reach its own particular bias voltage for the correct current. Those which need a higher voltage will take a little more time to ramp up from 0V.
The only thing I find odd is that the match seems to happen with the left and right pairs. In the circuit the valves are paired to work as outer and inner pairs and the valve matching should reflect that. One pair should be put in the two outer slots and one pair in the two inner slots. The idea is to keep the currents of the left side, (either a pair or a single valve), always matching the currents of the right side no matter what the power soak selection is. If we think of them as Left-Outer (LO) and Left-Inner (LI) and Right-Inner (RI) and Right-Outer (RO), for 20W the inner pair are switched off so we must make sure that we get LO = RO. For 40W we must make sure that LO + LI = RO + RI. i.e. the outer pair must be matched and the inner pair must be matched. (And of course if we have a full matched quad then it makes no difference where you put them when you first get them as they are all the same.)
What you are seeing suggests to me that the left two valves LO and LI, and the right two valves RI and RO, may actually be better matches than the inner and outer pairs which are the important thing. There are other factors in the circuitry which may be responsible for this little oddity but I would try the following test. Swap valves Left-Outer and Right-Inner, switch on and see what the TSC does. I would hope that now you would see the outer pair of LEDs work together and the inner pair work together meaning that the settling time has moved with the valves.
When you bought these valves were they two separate matched pairs or were they a full matched quad? If they are two separate matched pairs but with the pairs not actually matching each other, (I hope that is clear), is there a chance you have them in the wrong slots? I'll try to make all of this clear just in case.
Correct valve matching, (pairs are 'A' and 'B'):
- Code:
LO LI RI RO
[(A) (B)] [(B) (A)]
A = A (20W)
A + B = B + A (40W)
What you seem to have:
- Code:
----- 20W ----
/ \
[(A) (A)] [(B) (B)]
\ \ / /
----- 40W ----
You can see that, if both pairs 'A' and 'B' aren't a match to each other, this would not give a match for left and right bias voltages, though the joy of the TSC is that it tries to compensate for this to a degree.
If you swap LO and RI:
- Code:
----- 20W ----
/ \
[(B) (A)] [(A) (B)]
\ \ / /
----- 40W ----
The left and right sides now match for both 40W and 20W modes. Of course the 20W mode is the basis for the 5W and 1W modes too.
This isn't a huge issue and may not make any difference to things at all, it's just an oddity which is easily ticked off with just knowing your valve situation and by swapping a single pair. If it makes no difference or if it goes against what you know of your own valve matching, (I mean if you know you have the valves inserted in the correct sockets to give proper matching), then make sure to put things back as you had them after any investigation.
One last little bit of info, from H&K themselves, is that when you fit new valves the TSC takes some time to recalibrate itself to the new valves. For a couple of uses you may find that the TSC readings are off as it gradually adjusts itself from the settings for the old valves to the correct settings for the new set. People have reported this effect before and H&K confirmed it can happen.