Test Case rules cannot be created through standard 'New' rule form. Have to be created in context of rule instance for which you want to create test cases.
This is what help says:
Because test cases exist only in the context of unit testing a specific rule, you initiate creation of a new Test Case by clicking the Record Test Case button from the Test Cases tab of the rule you want to unit test. After running your unit test, click the Save Test Case button. In the Create form for the rule, you enter a name and a short description; the name that you enter is stored as the Purpose key part of the Test Case.
NOTE: You must have the AutomatedTesting privilege to be able to create Test Cases. For information about how to enable this privilege, see About Automated Unit Testing.
e.g.: for Activity rule you can create a test case by clicking 'Record new test case' button:
Could you provide details about the rule type for which you recorded test case? Anyways, I don't think results page needs to be updated manually to validate results. Could you provide more details on the need to update results page?