Didn't you read the warning?! "I show how it's made to educate and entertain,
not to replicate" (just kidding
)
But to be serious here, these experiments are potentially dangerous, especially since your ebay link is broken and we have no idea what high-voltage generator you are actually trying to use!
I don't want to discourage you, but I have a feeling you may be young and don't have the necessary experience jet to keep yourself save around high voltages. So please be cautious and keep in mind that you probably don't know all the dangers of high voltages.
And regarding your project it depends on how the outputs of your high-voltage generator are referenced, there are several different possibilities and I don't want to list them all. Assuming you're using a 'save' high-voltage generator, it would probably work pretty much regardless how you wire it, but worst case scenario would be that you shock yourself every time you're turning your device on/off or kill your high-voltage generator. So more info on the high-voltage generator would be helpful.
PS: Every "Negative ion generator" needs a high-voltage generator, but not every high-voltage generator is a "Negative ion generator"