What happens when someone you referred comes to Sylestia and notes that you referred them?

When you referred someone to sylestia, once they reach certain "check points", you will be given referral points that you can use to increase certain bonus in the game. you can go to account settings to see this.

They will need to reach a certain amount of battles, scales, and bred pets, each of which will give you 1 point. So the max points you can receive from 1 referral is 3 points.

With these points, you can increase the amount of gold you receive from battling, scales you receive from nurturing, or decrease the time it takes for your egg to hatch.