How do I force the "import" to be the first executed statement?

You can't (at least not with the desired arguments), because cacher->import(...) is being called after the module has been required — at which point any code of the module outside of subroutines will already have been run. That's how use works...

Update: it's maybe worth mentioning that import is not being called at all if you say use cacher ();. If that's an issue in your case, you might want to setup %cachehash with a default directory at the time the module is being required. Then, in case import is being called, just re-initialize %cachehash with the directory specified as the argument to use.  Kind of like this:

sub import {
    ...
    setup_cachehash($dir) if $dir;
}

sub setup_cachehash {
    ...
}

setup_cachehash("/tmp");  # default
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(From a performance point of view, doing things twice is of course suboptimal...)

P.S.: if you use Exporter in the same package, you probably want to explicitly call its import routine with the appropriate arguments (first arg = your package name), because normally the import method will be inherited from Exporter. In other words, Exporter's import will no longer be called (automatically) when you implement import yourself...