A professional plant breeder would cover the pistil (or most importantly, the stigma) of the flower before the flower opened and re-cover it after it had just been pollinated to prevent any insects from visiting it and affecting the cross. Insects can collect the pollen and they can drop pollen that is on their bodies from other flowers onto the stigma.
There is a diagram of the daylily flower parts at
http://www.daylilies.org/ahs_d...
Very few daylily hybridizers cover the pistils on the flowers they have pollinated. However a good strategy would be to take a careful look at the flowers on the plant that you pollinate. If the stigma is near the anther then covering the flower might be a good idea to prevent insects contaminating your cross. If the flower does not open fully and remains somewhat funnel shaped then again it might be a good idea to cover the flower. At least one daylily hybridizer removes all the petals from the flowers that they have pollinated. That is probably a good idea as it helps prevent insects from visiting that flower.
Although pollen placed on a stigma does not take very long to start to grow down and into the pistil, Stout found that the total time for a compatible cross to take or for the pollen to reach the ovules is 24 hours or less. During some of that time, if any other pollen is deposited on the stigma by insects that pollen will have an opportunity to compete with the pollen that the hybridizer had used.
Cultivars such as 'Stella de Oro' are often pollinated by insects visiting the flower.
One can get an idea of how often insects visit the flowers of particular daylily cultivars by watching to see if pods are set on flowers that have not been hand-pollinated. Of course, that is not possible if one dead-heads or removes the flowers after they close.
