The bleeding occurs when you put paint on a wet page. So they’ve already wetted the area where they want it to before putting the ink down on the page. In order to leave the eyes clear you have to not wet that area of the eyes. It sounds simple but it can be hard to see where you have painted the clear water on to the page and where you have left it clear for the eyes. You have to have really good lighting to see the clear water on your page.
Also, watercolor paper comes in different weights. So when painting wet into wet it is better to use a heavier weighted paper so that it holds more water in order to give you a longer “wet” time so that you to have more time to paint before the water dries.