How to convert product price in cart in mutator.php?

Question

1C-Bitrix

Hello!
Why is the cart price conversion that happens in mutator.php not visible in script.js? I do currency conversion in mutator

$result['BASKET_ITEM_RENDER_DATA'] = array();
foreach ($this->basketItems as $row)
{
    $rowData = array(
        'ID' => $row['ID'],
        'PRODUCT_ID' => $row['PRODUCT_ID'],
        'NAME' => isset($row['~NAME']) ? $row['~NAME'] : $row['NAME'],
        'FULL_PRICE' => $row['FULL_PRICE'],
);
$rowData["FULL_PRICE"] =  CCurrencyRates::ConvertCurrency($rowData["FULL_PRICE"], 'RUB', "USD");
$result['BASKET_ITEM_RENDER_DATA'][] = $rowData;
}

Next, in the basket template, I display the value from the array. It's available and I can get it. But when updating the quantity of goods in the cart, the amount is recalculated by ajax. I opened script.js and outputted everything contained in res.BASKET_DATA to the console, and so there is BASKET_ITEM_RENDER_DATA, but it contains the default values, and not changed by me.

1. Why does BASKET_ITEM_RENDER_DATA in script.js contain unchanged values?
2. How can I change them according to the metator principle?