Does the carbocation rearrangement in a SN1 reaction specify a change in degree?
The most common carbocation rearrangements involve [1,2] hydride or alkyl shifts. As a typical result a secondary carbocation is converted to a more stabilized tertiary carbocation.

In the course of these reactions, the migrating group and the positive charge change place, they move to opposite directions.

This is not the case in your example. 

I fail to see how your transformation can be described as a cationic rearrangement!