Yes they do.
In the nose of the rocket is a little thing called a “guidance system” It can change course anytime. This whole thing is stinky cheese. The reason NorthCom can tell us with certainty that there is no threat to the US is because they know exactly what happened. They just are not telling us.
Of course they do, until they are powerless ballistic objects, they do lots of course corrections while powered. And unless the film was sped up greatly, no way an airliner would leave a trail in such a short time.