Why belongsToMany association is not saved to joinTable?

I am new to php frameworks and I’ve started to learn cakephp few days ago, but even after reading cakephp cookbook about saving belongsToMany associations I still don’t know how to implement it in my situation.

I have three tables:
clients:
id | firstname | lastname | phone | email
interests:
id | text | comment | status_id | created_at
clients_interests:
client_id | interest_id

Models and entities were baked so I don’t think it’s something wrong there, but here is the code: ClientsTable.php

class ClientsTable extends Table
{            
    public function initialize(array $config)
    {
        parent::initialize($config);

        $this->setTable('clients');
        $this->setDisplayField('id');
        $this->setPrimaryKey('id');

        $this->belongsToMany('Interests', [
            'foreignKey' => 'client_id',
            'targetForeignKey' => 'interest_id',
            'joinTable' => 'clients_interests'
        ]);
    }

    public function validationDefault(Validator $validator)
    {
        $validator
            ->integer('id')
            ->allowEmptyString('id', 'create');

        $validator
            ->scalar('firstname')
            ->maxLength('firstname', 64)
            ->requirePresence('firstname', 'create')
            ->allowEmptyString('firstname', false);

        $validator
            ->scalar('middlename')
            ->maxLength('middlename', 64)
            ->allowEmptyString('middlename');

        $validator
            ->scalar('lastname')
            ->maxLength('lastname', 64)
            ->requirePresence('lastname', 'create')
            ->allowEmptyString('lastname', false);

        $validator
            ->scalar('phone')
            ->maxLength('phone', 24)
            ->requirePresence('phone', 'create')
            ->allowEmptyString('phone', false)
            ->add('phone', 'unique', ['rule' => 'validateUnique', 'provider' => 'table']);

        $validator
            ->email('email')
            ->allowEmptyString('email');

        return $validator;
    }

    public function buildRules(RulesChecker $rules)
    {
        $rules->add($rules->isUnique(['email']));
        $rules->add($rules->isUnique(['phone']));

        return $rules;
    }
}

InterestsTable.php

class InterestsTable extends Table
{
    public function initialize(array $config)
    {
        parent::initialize($config);

        $this->setTable('interests');
        $this->setDisplayField('id');
        $this->setPrimaryKey('id');

        $this->belongsTo('Statuses', [
            'foreignKey' => 'status_id',
            'joinType' => 'INNER'
        ]);
        $this->belongsToMany('Clients', [
            'foreignKey' => 'interest_id',
            'targetForeignKey' => 'client_id',
            'joinTable' => 'clients_interests'
        ]);
    }


    public function validationDefault(Validator $validator)
    {
        $validator
            ->integer('id')
            ->allowEmptyString('id', 'create');

        $validator
            ->scalar('text')
            ->maxLength('text', 128)
            ->requirePresence('text', 'create')
            ->allowEmptyString('text', false);

        $validator
            ->scalar('comment')
            ->maxLength('comment', 128)
            ->allowEmptyString('comment');

        $validator
            ->date('created_at')
            ->requirePresence('created_at', 'create')
            ->allowEmptyDate('created_at', false);

        return $validator;
    }


    public function buildRules(RulesChecker $rules)
    {
        $rules->add($rules->existsIn(['status_id'], 'Statuses'));

        return $rules;
    }


    public function getAll($id)
    {
        $connection = ConnectionManager::get('default');
        $results = $connection
            ->execute('SELECT i.*, s.name status_name, s.classname status_classname FROM interests i INNER JOIN clients_interests ci ON ci.interest_id=i.id AND ci.client_id=:client_id INNER JOIN statuses s ON i.status_id=s.id ORDER BY created_at DESC;', ['client_id' => $id])
            ->fetchAll('assoc');
        return $results;
    }
}

ClientsInterestsTable.php

class ClientsInterestsTable extends Table
{            
    public function initialize(array $config)
    {
        parent::initialize($config);

        $this->setTable('clients_interests');
        $this->setDisplayField('client_id');
        $this->setPrimaryKey(['client_id', 'interest_id']);

        $this->belongsTo('Clients', [
            'foreignKey' => 'client_id',
            'joinType' => 'INNER'
        ]);
        $this->belongsTo('Interests', [
            'foreignKey' => 'interest_id',
            'joinType' => 'INNER'
        ]);
    }


    public function buildRules(RulesChecker $rules)
    {
        $rules->add($rules->existsIn(['client_id'], 'Clients'));
        $rules->add($rules->existsIn(['interest_id'], 'Interests'));

        return $rules;
    }
}

Client entity - Client.php

class Client extends Entity
{         
    protected $_accessible = [
        'firstname' => true,
        'middlename' => true,
        'lastname' => true,
        'phone' => true,
        'email' => true
    ];
}

Interest entity - Interest.php

class Interest extends Entity
{          
    protected $_accessible = [
        'text' => true,
        'comment' => true,
        'status_id' => true,
        'created_at' => true,
        'clients_interest' => true,
        'status' => true
    ];
}

ClientsInterests entity - ClientsInterests.php

class ClientsInterest extends Entity
{

    protected $_accessible = [
        'client' => true,
        'interest' => true
    ];
}

And then in my controller I get all the data from a form. Interest entity after patchEntity() gets all its data besides client_id data for joinTable. And after save method new interest in interests table is created but there is no new row in clients_interests table. I’ve tried a lot of things from stackoverflow but it didn’t work because I can’t understand the mechanism of saving associated data even after reading the manual. Could anyone explain me in simple words how to save belongsToMany associated data? Here is the code of my save method in InterestsController.php:

public function add()
    {
        $this->request->allowMethod(['ajax', 'post']);
        $this->response->withDisabledCache();

        $interest = $this->Interests->newEntity();
        $interest = $this->Interests->patchEntity($interest, $this->request->getData(), 
            ['associated'=>['Clients._joinData']]
        );       

        if($this->Interests->save($interest)) {
            $result = ['error' => null, 'error_text' => 'SUCCESSFUL'];
        } else {
            $result = ['error' => null, 'error_text' => 'ERRORS ERRORS ERRORS'];
        }

        $result = ['error' => null, 'error_text' => 'ERRORS ERRORS ERRORS'];
        $this->set('result', $result);
        $this->set('_serialize', ['result']);
    }

And in my template I use this input for getting client_id:

<?php echo $this->Form->control('clients.0.client_id', ['hidden', 'type'=>'text','id'=>'client-id', 'class'=>'form-control']); ?>

Request data looks like this: https://i.stack.imgur.com/uQ1Rt.png
And Interest entity after patchEntity() looks like this: https://i.stack.imgur.com/iohL0.png

Also I wonder, what ‘clients_interest’ and ‘status’ fields were baked for? Is it wrong?