node.js async.series is that how it is supposed to work?

Not quite. You are executing the functions immediately (as soon as the array is evaluated), which is why they appear to start at the same time.

The callback passed to each of the functions to be executed is internal to the async library. You execute it once your function has completed, passing an error and/or a value. You don’t need to define that function yourself.

The final function never runs in your case because the callback function that async needs you to invoke to move on to the next function in the series never actually gets executed (only your callbackHandler function gets executed).

Try this instead:

async.series([
    takes2Seconds,
    takes5seconds
], function (err, results) {
    // Here, results is an array of the value from each function
    console.log(results); // outputs: ['two', 'five']
});