No one can see or access your mashed videos unless you share them. If you don't upload your videos to a social network, cloud service, or email them to someone else, they're only stored locally in your device within the 1SE album in your Photos app.
Where do the videos in the #1SEme tab come from?
The videos we show on the #1SEme tab are the ones our users post on Instagram using the #1SEme tag. These are only visible to us if our users have a public Instagram account.
So, don't worry! Otherwise nothing will be shared or seen by others.