That's a lot of code and you don't really show how you run it. In general you can run several AnyEvent timers at the same time:

use 5.010;
use strict;
use warnings;

use AnyEvent;

my $cv = AE::cv;
my $t1 = AE::timer 0.2, 0.2, sub { say "t1" };
my $t2 = AE::timer 1, 0, sub { say "t2"; $cv->send; };
$cv->recv;
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Perhaps you're blocking somewhere?