You only need to generate an OAuth token once, then can keep using the same one every time for logging into chat (the token is your password; ex. to login with an IRC bot, you might use ‘minnifutzi234’ as the username and ‘oauth:m7u1dhf6garrr39xinvwj0gy3fpkwr’ as the password).
The app only needs to be authorized once on each account also, because you can save the authorization code it gives you, and then use it for generating as many OAuth tokens as you need in the future. Then if you so desire, can use it to automatically request a new token each time using PHP (or your language of choice). Though I’m not sure why you’d want new ones each time, since this is all backend stuff being controlled by you, not through some 3rd party app, and since it greatly simplifies things to just keep using the same token.
Once you have a ‘chat_login’ scope’d OAuth token for each account, the rest can be done solely by chat commands, which means all you need is a small script that logs into each account (either sequentially, or all simultaneously) and sends the raw command PRIVMSG #channelName :/mod moderatorName (or /unmod to unmod).
And back to the TMI Chat OAuth Password Generator app. From what I can find, it sounds like the XSplit setup wizard uses its own app to authorize to your Twitch account (you can know for sure by checking which authorized apps are listed on your Twitch connections settings page), which should leave the TMI Token Gen app currently unused on the streaming accounts. It’s the app that everyone who uses Chatty or mIRC uses to get their chat login password.
Personally, I’d recommend just letting the TMI Token Gen app get the OAuth keys for you, then store each account’s OAuth token in the bot’s config file (that’s how most of us do it; it’s a pointless exercise to do it on your own for one-off projects like these).