The "rattle" could be what they call "buzz".

It is usually caused by not placing the finger just behind the fret and with all due respect to the person giving the spider walk lesson her finger placement isn't a good recommendation for where it should be and may be why you are getting that "buzz".

Here's a good way to get the position and pressure required just right. Of course a Google search will lead you to some you-tube videos on string buzz.

Place your finger just behind any fret and just touch the string gently and pluck the string. You will get that "dead" string sound. Gradually increase pressure until the string rings true. Take note of how softly you can press to get that sound. Any harder is a waste of effort and adds to finger soreness while learning.

Now move your finger up the fret so it is halfway between them and do it again. At some stage while increasing the pressure you will hear that "buzz" and it will require a lot more pressure on the string to get a clean note.

Hope this makes sense ....