Arghhh... Your code doesn't work! I fixed it as follows and there's no behavior you described:

package Wibble;
use Moose;

has 'thingies' => ( is => 'rw', isa => 'ArrayRef' );

package main;

my $w = Wibble->new( thingies => [ 'this', 'that' ] );
print join( ", ", @{ $w->thingies() } ) . "\n";
$w->thingies('another');
print join( ", ", @{ $w->thingies() } ) . "\n";

__END__
this, that
Attribute (thingies) does not pass the type constraint because: Valida
+tion failed for 'ArrayRef' failed with value another at (eval 69) lin
+e 7
    Wibble::thingies('Wibble=HASH(0x1274b38)', 'another') called at 74
+2018.pl line 10
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Update: and if you use $w->thingies(['another']); the last statement prints just 'another'.