我这里是这样处理的，你可以参考一下。
views:

<?php $form = ActiveForm::begin(); ?>
<?= $form->field($model, 'unitid')->dropDownList(
    Work::unitDataArr(),
    [
        'prompt' => '请选择单位',
        'onchange'=>'
            $.post("/work/lists?id='.'"+$(this).val(),function(data){
                $("select#work-department").html(data);
            });',
    ]
)->hint('用工单位，必选') ?>
<?= $form->field($model, 'department')->dropDownList(Work::dep(), ['prompt' => '请选择部门']) ?>
<?php ActiveForm::end(); ?>

Controllers:

    public function  actionLists($id)
    {
        $countDepartment = Empdep::find()
            ->where(['unitid' => $id])
            ->count();
        $departments = Empdep::find()
            ->where(['unitid' => $id])
            ->all();
        if ($countDepartment > 0) {
            foreach ($departments AS $department) {
                echo "<option value='" . $department->empid . "'>" . $department->depname . "</option>";
            }
        } else {
            echo "<option>-</option>";
        }
    }

<?= $form->field($model, 'username', [
        'inputTemplate' => '<div class="input-group"><span class="input-group-addon">@</span>{input}</div>',
])?>