The curl-7.38.0/lib/url.c has a code which sets value for CURLOPT_URL option:

  case CURLOPT_URL:
    /*
     * The URL to fetch.
     */
    if(data->change.url_alloc) {
      /* the already set URL is allocated, free it first! */
      Curl_safefree(data->change.url);
      data->change.url_alloc = FALSE;
    }
    result = setstropt(&data->set.str[STRING_SET_URL],
                       va_arg(param, char *));
    data->change.url = data->set.str[STRING_SET_URL];
    break;

The data->set.str[STRING_SET_URL] is not used nothere in libcurl code.
All the work is done using data->change.url value. (Which represents CURLINFO_EFFECTIVE_URL option of getinfo_char(), see curl-7.38.0/lib/getinfo.c)

But in Curl_follow() of curl-7.38.0/lib/transfer.c there is an assignment to data->change.url, which overwrites the value set previously.
There is also some other assignments exists too.

At the https://curl.haxx.se/libcurl/c/curl_easy_perform.html page there is the following note:

Just note that you will have to use curl_easy_setopt between the invokes to set options for the following curl_easy_perform.

But it is unclear if it is general requirement or only related to 'more than one file transfer', which requires to change file URL.

This is definitely a bug, still present in 7.54.1... Setting the URL in the handle should make it remain set like that for subsequent transfers done on the same handle.

My proposed fix for this bug and test case to verify it, are in #1632