use doesn't work that way. use always wants a bareword and not a variable as the module name. To dynamically load a module, use require:

...
    my $module_file = "$tmp.pm";
    require $module_file;
    $module_file->import(qw(%diary));
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Then you can even ditch the @INC hackery:

...
    my $module_file = "dir_$day/$userId.pm";
    require $module_file;
    $module_file->import(qw(%diary));
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