Since multi_query
(afaik) does not handle custom delimiters, the simplest way is probably splitting it into two separate, normal queries which do not need delimiters at all;
<?php
$mysqli = new mysqli('localhost', 'test', '', 'test');
$sql = "CREATE TABLE `test` ( `id` int(10) unsigned NOT NULL AUTO_INCREMENT PRIMARY KEY, emissione INT)";
$mysqli->query($sql);
$sql = "
CREATE TRIGGER `tr_insert_test` AFTER INSERT ON `test`
FOR EACH ROW BEGIN
UPDATE log SET dirty = 1 WHERE data = DATE(NEW.emissione);
END
";
$mysqli->query($sql);