The last paragraph of the terms of service is confusing, but I think I can explain this:
Long ago in the past, CCP had a game box cost for EVE Online. $59.99 for the box + monthly fees. They quickly reduced this to $5, but through the years they kept this $5 fee. Before the Alpha/Omega program, you could create a trial account, but to upgrade the account to full time cost you $19.99 for the first 30 days, followed by $14.99 monthly for the next sets of 30 days. There was this $5 fee embedded in there. They used to call it the Account Activation fee. And they offered various promotions, including the $5 starter packs, that basically just paid this fee + gave out free ships and a few days of game time.
With the change to the Alpha / Omega system, two things have happened:
They can’t call this $5 the “account activation fee” anymore because that doesn’t make any sense, so they’re calling it the “Omega fee”, which is quite confusing.
They switched PLEX from oldPLEX = $20 = 30 days of game time to newPLEX = $0.04 = 1 hr 30 minutes of game time = 1/500 of oldPLEX. So “500 PLEX” can be used to get 30 days of game time, and 125 PLEX = $5 can be used to just cover this “Omega fee” ; various promotion packs will offer smaller amounts of PLEX that I guess you can put together but not quite get the 500 you need for a full 30 day subscription.
So what they’re trying to say in the Terms of Service is that your buddy must pay for 30 days; he/she can either pay cash, or get the full 500 PLEX and apply it for game time. But if your buddy accumulates some promotion packs and/or less than the full 500 PLEX for the 30-days of game time, that lesser amount of PLEX won’t count and you won’t get your reward.
So, if you’re Omega, and your buddy upgrades with the full 500 PLEX for a full 30 days of game time, then you get 30 days of game time, and you can check your Account Management to verify that this game time was added. If your buddy goes Omega by paying cash (credit card), then you get 500 PLEX.