Hi, thank you for contacting JustAnswer.com. My name is Russell. I will do my best to provide the right answer to your question.
If the video shows everything to be just like your own Bernina's bobbin case and the place it fits into - everything of any major significance - then you need, if the procedure involves unscrewing and removing springs, then I would say, to put it back in, you need to remove them.
But! make quite sure the video's machine is indeed the same as your own model, before doing so. Following the wrong directions is bad.
Also: do you have a proper procedural instructions manual for your Bernina 880 ? because that would be, ultimately, the best resource to follow, as far as procedure for putting in the bobbin case again would go. So, in case it is of use to you, here is that Bernina 880 user guide/instruction manual:
and here also is the Tips (much shorter, 4 pages) for the 880's series, also:
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