In Yii 2, the main models and the related models are always fetched with the separated queries.
In the above, 2 queries will be executed. In the 1st query, leftJoin() and where() are used to filter the main models (members). It will find all the members with the status being 1 and having a post of id being 1. But the result set of the 1st query is not used to populate the related models. Instead, Yii will execute the 2nd query to get the related models(memberPosts). Because you have not specified any condition, the 2nd query will gather all the posts according to the definition of the relation.
This should work as expected:
$list = $this->find()
->leftJoin( // this is for the main models
'member_post',
['member_post.memberId' => 'member.id'])
->where([ // this is for the main models
'member.status' => 1,
'member_post.postId'=>1
])
->with([ // this is for the related models
'memberPost' => function($query) {
$query->where(['postId' => 1]);
},
])
->asArray()
->all();