Hello kevin,

after that Responsivizer is installed when the site is visited by mobile devices the template used is the mobile built in by default.

This is the same result that you get using the device emulator or using the string ?template=responsivizer to test.
You can choose to switch to a different mobile template acting on the parameter below (by default the built in template)
However notice that if you switch to a third party mobile template several features won't be available, such as modules management, exclusions, settings for layout, etc as discussed here http://storejextensions.org/faq/can-i-use-a-custom-mobile-template.html

John