The version of JRE packaged with each particular version of MVP is the one recommended for that particular version of MVP.  Versions later than the packaged version should work, but have not been tested. During an MVP client install, a check is made of the target system.  If a version of JRE is detected which is newer than the one packaged with the client, the included version will not be installed and the existing JRE version will be used instead.
If you want to change the JRE version after the MVP client is installed, reinstalling the MVP client is recommended.