As Paladin pointed out, this is a compile-time-versus-runtime thing. Furthermore, since you want to fully qualify all the module symbol names anyway, I see no reason to bother with any Exporter stuff.

File XYZ.pm:

# XYZ.pm

package XYZ;

use strict;
use warnings;

# require Exporter;
#
# our @ISA=qw/Exporter/;
# our @EXPORT_OK = qw/$PI CONST/;

our $PI = 355/113;
use constant CONST => 42;

1;
[download]

Output:

c:\@Work\Perl\monks\bliako>perl -le
"use strict;
 use warnings;
 ;;
 use lib '.';
 use XYZ;
 ;;
 print 'PI = ',   $XYZ::PI;
 print 'CONST = ', XYZ::CONST;
"
PI = 3.14159292035398
CONST = 42
[download]

(Disambiguation of  XYZ::CONST not needed here.)

Update: BTW: Doing a require in a BEGIN block
    BEGIN { use lib '.';  require XYZ; }
would have had the same phasing effect as the use statement.