Create a class to work with sending mail through customer.io on the path: protected/extensions/customerio/CustomerIO.php

And add the following code to it:

<?php

class CustomerIO extends CComponent {

    public $apiKey;
    public $siteId;

    /**
     * Default options
     * @var array
     */
    protected $defaultOptions = array(
        'user_id',
        //'first_name',
        //'last_name',
        'email',
        'type',
        'trigger'
    );

    protected $defaultValues = array();
    private $isSendMail = true;

    public function init() {
    }

    /**
     * Creates a customer in Customer.io
     * @param  mixed $customer_id You'll want to set this dynamically to the unique id of the user associated with the event
     * @param  array $attributes Extra customer info
     * @return void
     */
    public function createCustomer($customerId, $attributes) {
        if (!$this->isSendMail) {
            return;
        }
        $session = curl_init();
        $customerioUrl = 'https://track.customer.io/api/v1/customers/';
        curl_setopt($session, CURLOPT_URL, $customerioUrl . $customerId);
        curl_setopt($session, CURLOPT_HTTPAUTH, CURLAUTH_BASIC);
        curl_setopt($session, CURLOPT_HTTPGET, 1);
        curl_setopt($session, CURLOPT_HEADER, true);
        curl_setopt($session, CURLOPT_RETURNTRANSFER, true);
        curl_setopt($session, CURLOPT_CUSTOMREQUEST, 'PUT');
        curl_setopt($session, CURLOPT_VERBOSE, 1);
        curl_setopt($session, CURLOPT_POSTFIELDS, http_build_query($attributes));
        curl_setopt($session, CURLOPT_USERPWD, $this->siteId . ":" . $this->apiKey);
        curl_setopt($session, CURLOPT_SSL_VERIFYPEER, false);
        $resp = curl_exec($session);
        curl_close($session);
        if (strpos($resp, "Unauthorized request") !== false)
            throw new Exception("CustomerIo! Unauthorized request apiKey: $this->apiKey siteId: $this->siteId");
    }

    /**
     * Register an event in Customer.io
     * 
     * @param  mixed $customer_id You'll want to set this dynamically to the unique id of the user associated with the event
     * @param  string $name Event's name
     * @param  array $event_data Event data
     * @return void
     */
    public function trackEvent($customerId, $name, $eventData = array()) {
        if (!$this->isSendMail) {
            return;
        }
        $session = curl_init();
        $customerioUrl = 'https://track.customer.io/api/v1/customers/' . $customerId . '/events';
        $data = ['name' => $name, 'data' => $eventData];
        curl_setopt($session, CURLOPT_URL, $customerioUrl);
        curl_setopt($session, CURLOPT_HTTPAUTH, CURLAUTH_BASIC);
        curl_setopt($session, CURLOPT_HEADER, false);
        curl_setopt($session, CURLOPT_RETURNTRANSFER, true);
        curl_setopt($session, CURLOPT_VERBOSE, 1);
        curl_setopt($session, CURLOPT_CUSTOMREQUEST, 'POST');
        curl_setopt($session, CURLOPT_POSTFIELDS, http_build_query($data));
        curl_setopt($session, CURLOPT_USERPWD, $this->siteId . ":" . $this->apiKey);
        curl_setopt($session, CURLOPT_SSL_VERIFYPEER, false);
        $resp = curl_exec($session);
        curl_close($session);
    }

    /**
     * Checking for required fields
     * 
     * @param array $options user data
     * @param array $defaultFields required fields
     * @return type
     * @throws HttpException
     */
    protected function testDefaultOptions($options, $defaultFields = array()) {
        if (!$this->isSendMail) {
            return;
        }
        $createCustomerOptions = array();
        if (empty($defaultFields)) {
            $defaultFields = $this->defaultOptions;
        }
        foreach ($defaultFields as $defaultField) {
            if (!isset($options[$defaultField])) {
                throw new HttpException(501, __CLASS__ . ' no default field [' . $defaultField . ']');
            }
            if (!in_array($defaultField, ['trigger', 'user_id'])) {
                $createCustomerOptions[$defaultField] = $options[$defaultField];
            }
            if (isset($this->defaultValues[$defaultField])) {
                $createCustomerOptions[$defaultField] = $this->defaultValues[$defaultField];
            }
        }
        return $createCustomerOptions;
    }

    /**
     * Send Mail
     * 
     * @param array $options
     * @param array $createCustomerOptions
     * @return type
     * @throws Exception
     */
    protected function send($options, $createCustomerOptions = array()) {
        if (!$this->isSendMail) {
            return;
        }
        if (empty($createCustomerOptions)) {
            $createCustomerOptions = $this->defaultOptions;
        }
        try {
            $createCustomerOptions = $this->testDefaultOptions($options, $createCustomerOptions);
        } catch (Exception $e) {
            throw $e;
        }
        if (!isset($options['created_at']) || empty($options['created_at'])) {
            $options['created_at'] = time();
        }
        $this->createCustomer($options['user_id'], $createCustomerOptions);
        $this->trackEvent($options['user_id'], $options['trigger'], $options);
    }

    public function sendMail($options = array()) {
        $this->send($options);
    }

}

Add the extension and its settings in file protected/config/main.php:

//...
    'components'=>array(
        //...
        'customerio' => array(
            'class' => 'ext.customerio.CustomerIO',
            'siteId' => '<YOUR SITE ID>',
            'apiKey' => '<YOUR API KEY>',
        ),
    ),
//...

Change siteId and apiKey on their own and start to use it. Example:

Yii::app()->customerio->sendMail(
    array(
        'first_name' => 'FirstName',
        'last_name' => 'LastName',
        'email' => 'example@example.com',
        'user_id' => '1',
        'trigger' => 'test',
        'type' => 'event'
    )
);

Or add a method to the class:

public function testSend($data = array()) {
        //...
        $options = array(
            'trigger' => 'test',            
            'type' => 'event',
            'first_name' => 'FirstName',
            'last_name' => 'LastName',
            'email' => 'example@example.com',
            'user_id' => '1',
            //...
        );
        $this->send($options);
    }

Call it in the right place as follows::

Yii::app()->customerio->testSend($data);

For those who work with Yii2, remake this class will not be difficult.