我解决了我的问题，而且令人尴尬的是，它实际上既不是axios也不是服务器相关的。
这个问题源于我在下面的例子中用粗体显示的一个const关键字（例子下面的解释）：

const axios = require('axios');
const axiosObjs = {};

async function get_data(dataSetName) {

    let dataToSave = [];

    if (!axiosObjs[dataSetName]) {
        axiosObjs[dataSetName] = axios.create({
            method: 'get',
            url: 'https://example.com/dataSets/',
        });
    }

    for (let i = 0; i < 10; i++) {
        const urlString = 'https://example.com/dataSets/' + dataSetName + "_" + i;

        **const** dataSetChunk = await axiosObjs[dataSetName](urlString)
            .then(result => result) 
            .catch((err) => { return "this is just a simplified example"; });

        dataToSave = [].concat(dataToSave, dataSetChunk.data);

        await wait_milliseconds(500);  // made up function, waits half a second
    }
    
    save_data_to_file(dataSetName, dataToSave);  // made up function, saves data to file
}

// these all result in data mixed up between saved data sets
get_data("dataSet1");
get_data("dataSet2");
get_data("dataSet3");

当我创建简化的示例发布在StackOverflow上时，我在定义dataSetChunk常量时包含了const关键字。但在实际代码中，我不小心没有包含const关键字，JavaScript是JavaScript，它只是继续将dataSetChunk作为全局变量。当然，它是一个全局变量，这意味着所有同时发生的函数调用在从服务器填充数据时共享同一个变量。

const axios = require('axios');

async function get_data(dataSetName) {
  let unordered_data_chunks = [];
  let promises_to_await = [];

  for (let i = 0; i < 10; i++) {
    let data_source_url = 'https://example.com/dataSets/' + dataSetName + "_" + i;

    let promise = axios.get(data_source_url)
      .then((res) => {
        let data_chunk = {
          index: i,
          data: res.data
        };
        unordered_data_chunks.push(data_chunk);
      })
      .catch((err) => {
        // Do something to handle error.
      });

    promises_to_await.push(promise);
  }

  await Promise.all(promises_to_await);

  let ordered_data_chunks = unordered_data_chunks.sort(
    (a, b) => a.index - b.index
  );

  let data = ordered_data_chunks.reduce(
    (accumulator, current_value) => {
      accumulator.push(current_value.data);
      return accumulator;
    },
    []
  );

  save_data_to_file(dataSetName, data);
}

get_data("dataSet1");