As far as I am aware the turnitin software percentages only offers them a reasonable suspicion at which point they will take the paper and look at it individually. If you made the 'mistake' of submitting the wrong paper then I can't see how turnitin is relevant at all. The problem start when and or if they suspect you might have tried passing some work off as your own and are then suspected of attempting to cover this up by fabricating a mistake defence. It really depends on what, if anything, they suspect.
As the above posters, if your mistake is genuine then you have nothing to fear. Tell the truth in the meeting and they will probably come up with an agreeable solution.