You could use unless control structure to execute the code in the block just upon successful mount:

use strict;
use warnings;
use File::Copy;

my $usbdev = "/dev/sdb1/";
my $usbmount = "/media/usb/";
my @files = qw( file1 file2 file3 ); # or read from the filesystem usi
+ng a glob or directory handle

unless ( system "mount $usbdev $usbmount" ) {
    # Return was zero - meaning success
    for my $file (@files) {
        copy($file,$usbmount) or warn "Failed to copy $file: $!\n";
    }
    ! system "umount $usbmount" or die "Can't umount $usbmount\n";
}
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