@nicomilie: What you describe—that the images are uploaded to the account associated with the credentials you’re using to make the requests—is expected behavior.
You need to use the additional_owners parameter when making a request to the POST media/upload endpoint to be enable another user to use the media. The additional_owners parameter allows you to specify the user(s), by user_id, who are allowed to use the media. Please see the example request below:
$ twurl -X POST -H upload.twitter.com "/1.1/media/upload.json?additional_owners={additional_owners}" --file image.jpg --file-field "media" | jq
{
"media_id": 790053336116453400,
"media_id_string": "790053336116453376",
"size": 96203,
"expires_after_secs": 86400,
"image": {
"image_type": "image/jpeg",
"w": 900,
"h": 360
}
}