I've had Natilla many times in the past at my favorite Cuban restaurant, and I've also made it myself in the past. I don't like the sound of the recipe you posted, and the photo doesn't look right, either - the custard looks very lumpy, and it should be completely smooth. Unfortunately, I no longer have the recipe I used, but I know that most Natilla recipes use egg yolks only and no whites, plus a little cornstarch to thicken it.
I have 2 recipes in my files from very reliable sources. If you'd like, I can find the links and post them here. I haven't tried these recipes yet, but I trust the sources.