Alright, after spending almost all day with some research, I guess the issue has something to do with the new API. My knowledge is very limited so I'll wait for the new Simple Fields update.
Meanwhile, I've come up with a quick fix that I'd like to share, just in case someone need to have WP latest version running with TinyMCE in Simple Fields like me.
I uncheck "Use HTML-editor" check box and add manually add TinyMCE using the snippet from the tutorial here:
Paste the code in functions_post.php, under the close bracket of "echo $media;"
Then TinyMCE should appear, and you'll run into another problem when trying to insert an image from the library but thanks to cm258 from this post:
The thing is, in WordPress 3.3, wp_tiny_mce() is deprecated so I'm not very happy with this dirty fix but it's working so far so hopefully the real fix from Simple Fields will come out soon.
Thanks to Pär Thernström for the great plugin though!