Hi,
These three voltages --- these three in particular --- are used only by the plugins. These supplies each has an independent return line, and independent sense lines leading back from the plugin. The regulator circuit regulates the voltage at the other end of the sense lines, not the supply voltage on the regulator board. The regulator, however, has diodes that conduct from supply line to sense line when there is no voltage on the sense line (when the plugin isn't installed), so that the regulator is always working. So, first, double check how you're making the measurements. Are you measuring between the sense line test points on the regulator board, or between the regulated output voltage and chassis ground? The latter won't give proper readings because it's not at exactly the same potential as the return path.
But, yes, the three supplies are (sort of) coupled together. The +20 V supply is used as the reference for the -40 V regulator. The -40 V regulator sets its output to -2.0x the +20 V supply. In the schematic you can see the -40 V adjust trim pot whose wiper feeds the controlling op amp is part of a voltage divider between the +20 V and -40 V regulated output rails. Instability of the +20 V supply will be exactly mimicked by the -40 V supply *-2.0 (if that's happening it means the -40 V regulator is working perfectly).
The -10 V supply uses the -40 V regulated output and some zener diodes to set up a reference voltage against with the output of its trim pot is compared (which is forming a voltage divider across the sense lines). So ... small fluctuations in the -40 V supply will produce small changes in the current flowing through the zener diodes, but shouldn't change the voltage drops across them to 1st order, should be a higher order effect. If you're seeing fluctuations at 1 part in 1000 on the -40 V supply I wouldn't expect to see fluctuations at that same level in the +10 V supply. Maybe 1 part in a million. There will be a coupling, but you should have to make a super careful measurement to see it.
For that reason I think what you're seeing is due to measurements w.r.t. the wrong reference potential (e.g., chassis ground instead of the return line).
PS --- you (or somebody else) wouldn't happen to have complete + readable schematics for the regulator? I'm trying to debug a problem in my own, but none of the service manuals floating around on the internet that I've found are both readable and complete. You can choose readable or complete, but not both.