You solve it by signing the image. Sometimes you just won't be able to get a completely reproducible build processes that's fully deterministic, so Nix cannot fix this problem entirely. Additionally, sometimes you just don't have time, or experience to take another program/tool you didn't write and package it up such that it never downloads things from the internet.
It's a hard problem to solve, and Nix helps a lot, but it's not going to fix all the problems, which is why we should care more about trusting the packager to package something relatively reproducible and sign it so that we it can be vouched for.
Images are nothing but a caching technique for the results of deterministic builds.
If you're using them for any other reason, you have a flawed process that is going to come back to bite you some day.