Incorrectly filled _lft _rgt when changed parent_id for 2+ models

[Nhemas]

As example I receive 2 requests, which must change parent_id of 2 models. Prev and new parent_id are different but same for both models. But sometimes i see when _lft and _rgt filled incorrectly. There are 3 possible outcomes: 1. both models have same lft rgt 2. both parents rgt lft cross each other, example: 1-210, 200-211 3. everything ok
It seems like ordinary problem with parallel queries, but somehow i cant resolve it. I tried: 1. add lock table 2. set isolation level to serializable 3. add ->fixTree() at the start and the end of transaction 4. all together
I think the problem happens here. $inputData has only parent_id.

DB::transaction(function () use ($inputData, $model) {
    $model->fill($inputData);
    $model->save();
}

Cant understand why transaction didnt help, I dont think model additionally changes somewhere else