Pay attention since there are two versions of mongodb drivers for php. Mongodb 3.2 requires the mongodb.so driver version, which is different from mongo.so (and now deprecated).
Also, as mentionned in the mongodb.so documentation on php.net :
Application developers should consider using this extension in conjunction with the MongoDB PHP library [...]
This official library provides the usual mongodb CRUD functions, on top of the new mongodb.so driver, and the librarie's documentation also says you can make use updateMany() as you would do it in javascript:
$updateResult = $collection->updateMany(
["inspector" => "J. Clouseau", "Sector" => 4 ],
['$set' => ['Patrolling' => false]]
);
printf("Matched %d document(s)\n", $updateResult->getMatchedCount());
printf("Modified %d document(s)\n", $updateResult->getModifiedCount());