@RestControllerAdvice and @ControllerAdvice together

I have an Spring MVC application which has @Controller s and @RestController s. I was thinking that: When I have some Exception at my @Controller, It gonna be handled by my @ControllerAdvice and when I have some Exception at my @RestController, It gonna be handled by my @RestControllerAdvice... But now I think It's not how things should work, because my @ControllerAdvice are catching everything, even any exception that is thrown by @RestController...I do not know if this should happen. Here my code:

 @ControllerAdvice
 public class ExceptionHandlerController {

 private final String DEFAULT_ERROR_VIEW = "error/default";

  @ExceptionHandler(Exception.class)
  public ModelAndView defaultErrorHandler(HttpServletRequest req, Exception e) 
  {   
      ModelAndView mav = new ModelAndView();
      mav.addObject("exception", e);
      mav.addObject("danger", e.getMessage());
      mav.addObject("url", req.getRequestURL());
      mav.setViewName(DEFAULT_ERROR_VIEW);
      return mav;
  }
}


@RestControllerAdvice
public class ExceptionHandlerRestController {

  @ExceptionHandler(Exception.class)
  public ResponseEntity<String> defaultErrorHandler(HttpServletRequest req, Exception e) throws Exception {
      return new ResponseEntity<>(" test "+e.getMessage(), HttpStatus.INTERNAL_SERVER_ERROR);        
  }    
}