Diagnosis
You didn't mess up—this is flash rust, and it's normal on bare steel after its first exposure to heat and moisture if the oil coating wasn't perfectly even or thick enough.
How to Fix It
Don't panic. Just do another round of seasoning. Heat the smoker up to around 250-275°F. Apply a very thin, even coat of a high-smoke-point oil (like canola, grapeseed, or flaxseed) to all interior surfaces using a rag or paper towel. Let it smoke for an hour or two, then let it cool. The oil will polymerize over the rust, sealing it. You might need to do this 2-3 times.
If That Didn't Work
If the rust is thick or scaly, you may need to lightly sand the area with fine steel wool (like 000 grade) to knock off the loose bits before reapplying oil. The goal is to get back to bare, smooth metal before seasoning.
Heads Up
Never use cooking spray (Pam) for seasoning—the propellants and additives can leave a sticky residue. Plain liquid oil is the way. A little rust here and there won't hurt the food, but you want a stable, blackened seasoning layer for protection.