CSVファイルをSJISで読み込むほうはよく出るのですが、
出力するほうは意外と誰も書いてなかったので私が書きます。

こうする

document_root/includes/csv.class.php

<?php

//use League\Csv\Reader;
use League\Csv\Writer;
use League\Csv\CharsetConverter;

require dirname(__FILE__) . '/../third_party/league/csv/autoload.php'; // 適宜読み込み先を変更すること。composerとかで読み込んでたら記述いらんかも

class csv
{
  public function __construct()
  {
    //
  }

  /**
   * Export csv as SJIS-win by League/CSV
   *
   * @params string $fileName e.g. "example.csv"
   * @params array $records e.g. [[1, "山田太郎", 80]]
   * @params array $rowHeader [optional] e.g. ["連番", "氏名", "年齢"]
   * @return void
   * @link https://csv.thephpleague.com/9.0/
   */
  public function export($fileName, $records, $rowHeader = [])
  {
    // SJIS-winで出力
    $encoder = (new \League\Csv\CharsetConverter())->inputEncoding('utf-8')->outputEncoding('SJIS-win');

    $csv = \League\Csv\Writer::createFromFileObject(new \SplTempFileObject());

    $csv->addFormatter($encoder);

    // 見出し行
    if(is_array($rowHeader) && count($rowHeader) > 0){
      $csv->insertOne($rowHeader);
    }

    // データ行
    foreach($records as $record){
      $csv->insertOne($record);
    }

    $csv->output($fileName);
    exit;
  }
}

document_root/index.php

require dirname(__FILE__) . '/includes/csv.class.php';

$csv = new csv();

$fileName = "ファイル名.csv";
$rowHeader = ["み","だ","し","行"];
$records = [
  ["な","か","み","1"],
  ["な","か","み","2"],
  ["な","か","み","3"]
];

$csv->export($fileName, $records, $rowHeader);

参考URL

https://csv.thephpleague.com/9.0/converter/charset/
https://qiita.com/kiyc/items/f70280e13e5194e5dd94