There are two possible workarounds:

A string eval, e.g.

my $subst = 'lc $1';
# and later
$str =~ s{$pattern}{push @pos, pos $str; eval $subst; }eg
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The other one moves the push to the regex:

use strict;
use warnings;
use Data::Dumper;

my @pos;
my $str = "foobarbaz";

if ($str =~ s{([aeiou]+)(?{ push @pos, pos $str })}{<--$1-->}g){
    print Dumper \@pos;
    print $str, "\n";
}
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But please read the notes in perlre on the (?{...}) construct.