Сделай три модели:
В Problems: $this->hasMany(ProblemsHasOrgan::className(), ['organ_id' => 'ID'])
В ProblemsHasOrgan: $this->hasOne(ProblemsOrgan::className(), ['ID' => 'problem_id'])
И все!
$problems = Problems->find()->with('ProblemsHasOrgan')->all();
foreach($problems->getProblemsHasOrgan->all() as $one)
{
echo $one->problemOrgan->name;
}