An imperative program is analogous to how a Turing machine works?
At a high enough level and when contrasted with functional programming, sure. Turing machine models and imperative programs have in common that they start from an input and take a series of steps that change a state stored in memory, ending with some output.

This contrasts with lambda calculus and functional programming which generally and loosely do not have the above features.

I think reading any more into the comparison than this, or trying to take it any farther, is probably a mistake. As Yuval says, Turing machines are quite different from modern machines and program execution environments.