Hmm not sure what's wrong in your setting...

I ran a quick test on my mobile, and this works for me.

Probably an issue with Exporter ?

 
use v5.12;
use warnings;

BEGIN{
  package log;
  our $var= "default";

  sub tst { say $var }
  
  # export
  *::var = *var;
  *::tst = *tst;
}


package main;
our $var;
{
  local $var = "foo";
  tst();
}

tst();
[download]

perl local_import_var.pl
foo
default
[download]

Anyway I'd rather recommend another design, like using caller to get the function's name or setting a regex to parse the message for keywords.

HTH :)

EDIT

AHH, got it. What exporter does is to only export the scalar slot, which is causing your problem.

*::var = \$var; # replace!

Effect:

perl local_import_var.pl
default
default
[download]

So exporting the whole typeglob will fix it.:).

In case exporter doesn't support * , use your own import