New cast iron skillet came out rusty after seasoning
That looks a lot more like cooked oil than rust on the inside. Either way, probably not rust, and definitely not enough rust to cause concern. Scrub it off.

When I season my cast iron, I just do it on the stove. I heat the pan until it's smoking, and carefully add a little oil and swirl it around. Let it cool, wipe it out. Then, use it. When you do use it, clean it gently. Avoid using soap, just use water and a spatula or something. It's a good idea to heat it on the stove top to dry it well after cleaning. Over time you get a good thing going. 

But either way, rust with cast iron is no cause for concern. Even if it was completely covered in rust, you can brush it out and re-season.