The referral rewards don't update until you reach the first reward tier (5 level 10+ summoners). When you have enough referrals to get the first reward, the levels will update.

The system still tracks every referral you send in, it just doesn't update until you reach the first tier, so they display as level one, you can check their level by just looking up their profile.

I set up a bot to create accounts referring my account. If there was no level requirement, I'd have a plane ride to Riot Games in about two weeks time. Level ten shows that your recruit played the game long enough to be partially invested into the game (iow, wasn't a referral program smurfer.