Did you check the PCR product on a gel before cloning to see that it was the right size? It could be that your primers amplify something other than your intended product. Another possibility is that if you used a plasmid for your PCR template, that's actually what your cells are being transformed with instead of the intended vector. (It doesn't take much DNA to transform DH5a or DH10B, they're highly competent.)

Are you sure that there's no tetracycline-controlled element present on your plasmid? It is actually quite common to have an element on the plasmid to control your gene's expression.

Are you sure that you used the correct primers for sequencing?

Unfortunately, I never used gateway cloning, so I don't know what problems one might be confronted with. Could it be that another plasmid was present in your ligation sample?

Hi Abbey, do you or does anyone in your lab work with the tetracycline inducible system? In my experience, I've noticed that sometimes plasmids we tend to work with frequently end up as contaminants in a lot of experiments. I have had issues with this before and my lab ended up designating a bench as a "plasmid-free zone" to solve the issue of contamination in things like PCRs/qPCRs. This might explain why you're seeing that gene in your colonies.

Also, I have to ask - in your transformation protocol you've mentioned shaking the bacteria at 37 degrees C for 1 minute. I'm assuming this is a typo and you meant 1 hour?