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The reality altering feature of the device is a 5 step process.

Step 1. It operates just as it would of without the feature.

Step 2. It makes a backup of the memories it's current user.

Step 3. It removes it's self from reality. This causes a tear in causality that reality must repair.
With the device gone nothing caused the changes it made, if nothing caused the changes then no change must of occurred. Thus like that the past ends up changing to reflect the current present.

Step 4. The device returns to our reality in the possession of the person who used it.

Step 5. The device takes the current memories of it's user, mixes them with the backup from step 2 and gives it all back.

Now why are steps 2 and 5 so important ? Good question.

Let's say you swapped bodies with your sister; the past changes, now suddenly you remember growing up as your sister, going to school as your sister and just living your entire life as her with no memories of it ever having been any other way.
Who are you ? Are you "you" or are you your sister ?

The mind is almost exclusively made up of your past experiences and memories.
In this example your mind would become 80% the same as your sister's prior to swapping bodies with her. Similarly your sister's mind is now 80% "your" mind. This is what allows people you swapped with to so flawlessly continue living as "you".

Steps 2 and 5 are required so that you can go back to being "you" after step 3.
If you were to swap 2 people other than yourself, their minds would become 80% each other and there wouldn't be any significant changes in behavior.