When working under the eyes, have your model look upwards - only with the eyes, without moving the head. If you work above the eyes (eyelid), have your model close his/her eyes in a relaxed manner.
Children are inclined to shut their eyes tight. Then you can say: keep your eyes closed as if you are sleeping.
If you do not want the colours to mix, be sure to wait for the first layer to dry before applying another colour over it or up against it.