I've never seen a tattoo that looked blown out and then later looked normal, but maybe someone else has.
Listen, EVERYONE is telling you to calm down and let it heal. AFTER it heals, in 6-8 weeks, you'll know what it will look like. Here's the thing - You can't fix blow-outs, so it doesn't really matter if it's blown out or not. No, they are NOT normal, but they do happen. It's not always the artist's fault, they tend to happen more on thin, delicate skin.
Tattoos are not perfect. I've never seen a tattoo that you couldn't find something wrong with if you looked hard enough. If perfection is your goal, I wouldn't get any more.