The electrons in this experiment are accelerated through a voltage of 150 - 300V, according to the manual. That's about 100 times higher than the energy in a visible photon. It's also much more than the (comparable) ionization energy of Helium. Considering the energy of the electrons is only varying by a factor 2 and it is far greater than the obvious energy scales involved, one wouldn't expect the spectrum to change significantly with the voltage.
Presumably, all of the lines are emitted in a proportion such that they look cyan overall.
The sky does not skip over the green range of frequencies. The sky is green. Remove the scattered light from the Sun and the Moon and even the starlight, if you so wish, and you'll be left with something called airglow (check out the link, it's awesome, great pics, and nice explanation).
Because the link does such a good job explaining airglow, I'll skip the nitty gritty.
So you might be thinking, "Jim, you half-insane ceiling fan, everybody knows that the night sky is black!" Well, you're only half right. The night sky isn't black. The link above explains the science of it, but if that's not good enough, try to remember back to a time when you might have been out in the countryside. No bright city lights, just the night sky and trees. Now when you look at the horizon, can you see the trees? Yes, they're black silhouettes against the night sky. But how could you see black against black? The night sky isn't black. It's green thanks to airglow (or, if you're near a city, orange thanks to light pollution).
Stop, it's picture time. Here's an above the atmosphere view of the night sky from Wikipedia:
And one from the link I posted, just in case you didn't check it out:
See, don't be worried about green. The sky gets around to being green all the time.
Best Answer
The color of the photon is related to its frequency $f$, which can be related to the energy of the photon by the expression $E = hf$, where $h$ is Planck's constant. Thus the different colors of the emitted photons describes their different energies.
The next step is to determine why specific elements emit certain colors. This has to do with the different energy levels of the electrons "orbiting" the nucleus. When an electron drops from a high energy orbital to a low energy orbital the difference in energy results in an emitted photon. There are many rules regarding the allowed transitions, hence the allowed energy of photons that are emitted, and these vary by element. What you are observing are the allowed transitions of each specific element.