Can a new users must login through .salesforce.com instead of test.salesforce.com?

This is a known issue still unfixed and faced by many people like you.

Summary

After a sandbox has been activated, it may take up to 5 hours for login attempts via the test.salesforce.com login portal to be successful. This is due to a delay in the replication of the user from the new sandbox environment to the redirection pointer on the test login server. In some scenarios, the replication delay seems to also occur when creating new users in a sandbox environment.

Repro After your sandbox has been refreshed, attempt to log into the environment from Test.salesforce.com. After several hours, the login attempts will be successful once the replication has completed.

Workaround The current workaround is to log into the application directly from the server in which this sandbox environment is hosted. This will bypass the test login server completely. To login directly to the server, access the login page for the server itself. For example, if you organization resides on the cs5 environment you would log in via https://cs5.salesforce.com. If you are using My Domains and not sure which server you should be accessing, please define the domain for the environment into the field on this page.