Updated OS information.

Really need that repro script because as far as I can tell from that code, it should not repro your problem. Which is what you said is the case. But it looks like what you've given should be close?

By the way, there's a bug in your code:

  if ($errno && error_reporting()) {

That's a boolean &&. What the expression does is check that $errno != 0 (the expression was not @-silenced) and that error_reporting() != 0. What you should be doing is checking that the error_reporting() bitmask has the $errno bit set - using the bitwise &. An easy mistake/typo to make.

  if ($errno & error_reporting()) {

Thank you for you comment. I able to reproduce the bug, here is a code:
<?php
class MyHandler {
    public function handleException(\Throwable $e) {
        die('This line WILL NOT be called!');
    }

    public function handleError($errno, $errstr, $errfile, $errline, $context) {
        if ($errno & error_reporting()) {
            // This line should cause the MyHandler::handleException() be called
            // but the the die() in the $myCallback is executed instead,
            // it should not happen!
            throw new \ErrorException($errstr, 0, $errno, $errfile, $errline);
        }
    }

    public function shutdown() {
        die("\n" . __METHOD__ . ' called');
    }
}
error_reporting(E_ALL | E_STRICT);
ini_set('display_errors', 1);
$myHandler = new MyHandler;
set_error_handler([$myHandler, 'handleError']);
set_exception_handler([$myHandler, 'handleException']);
register_shutdown_function([$myHandler, 'shutdown']);

// ------------------------
// In some method of some class:
class MySomeClass {
    public function test() {
        $method = 'doSomething';
        $res = $this->$method();
    }

    public function doSomething() {
        // ...
        $myCallback = function ($name) {
            die('This line WILL be executed!');
        };
        foreach (['a', 'b', 'c'] as $item) {
            // ...
            try {
                // Trigger error - E_WARNING
                $res = $myCallback();
            } catch (\Throwable $e) {
                die('This line WILL NOT be executed');
            }
            die('This line WILL NOT be executed');
        }
    }
}

$instance = new MySomeClass();
$instance->doSomething();

-------------------------------------------------------------
Part of the output is:
This line WILL be executed!PHP Fatal error:  Uncaught ErrorException: Missing argument 1 for MySomeClass::{closure}(), called in ... on line 44 and defined...
...

https://3v4l.org/haASA

So the problem is that the function gets executed even if there is an exception thrown during the call.

The main problem here is that the return value of http://lxr.php.net/xref/PHP_TRUNK/Zend/zend_execute.c#896 was inverted. Furthermore http://lxr.php.net/xref/PHP_TRUNK/Zend/zend_vm_def.h#4717 does an unconditional HANDLE_EXCEPTION() in the failure case, even though the warning does not necessarily result in an exception. Should probably issue ZEND_VM_NEXT_OPCODE_CHECK_EXCEPTION() in the failure case.