Here's one way (BTW. Using backticks and ignoring the output doesn't make a lot of sense):

use threads;
use threads::shared;

my % commands = (
    CMD1 => process 1,
    CMD2 => process 2,
    CMD3 => process 3,
); 

foreach my $cmd(keys %commands) {

    my $done :shared = 0;
    async {
        `$commands{$cmd}`;
        if($?) {
            print ¨ Error:  $commands{$cmd}\n¨;
        }
        $done = 1;
    }->detach;

    until( $done ) {
        for( 1 .. 60 ) {
            sleep 1;
            last if $done;
        }
        print ¨Still executing: $command{$cmd}\n¨
    }
}
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