If I understand correctly, you tried to hook the cabinet lighting
transformer into same circuit as kitchen main lighting, right? And
you have multiple switches there? And the box you tapped into houses a
3-pole switch fed with a 3-conductor cable?? It is not a 220V circuit
- so did you wonder why there would be a 3-conductor there? It is more
expensive, so an electrician will not use it unless needed.
A bit of trivia: hook a meter in series with a 40-60 watt lightbulb and
check voltage on the meter. Chances are, you'll get around 50-60
volts. Most meters are ranged to 400mA and a 60W bulb draws about
500mA. In series, they will split voltage about in half.
I had a similar problem long ago when wanting to install a new outlet
and I found a very convenient cable running in the wall right where I
wanted the outlet. Tapping into cable revealed 3 wires. Not giving
it much thought, I wired outlet between black and white, only to get an
outlet that would not work at all or have VERY low power at - guess what
- about 50 volts. Was dumbfounded until I traced all wires and found
out I tapped into a traveler running between top and bottom staircase
Really, I also had theories about capacitance, EMF, ESP, stray
currents, and other exotic stuff, while in truth I simply had it wired
in a series with a lightbulb. Trace your wires. Looks like the box
you hooked into is final on a power-through-fixture chain.