If you are using ClearPass, you can configure that in the Web Login or for Self-Registration in the NAS Settings:
For Aruba controller it can be configured in the L3 Authentication Captive Portal profile under 'Redirect URL'; this setting overrides what ClearPass might be configured to. So either use ClearPass or do it on the controller.
For Instant the Redirect URL is part of the captive portal configuration.
By default, the original URL is recorded so if people manually enter a site in their browser that after authentication they end up on that site. In practice, the operating system will detect if there is a captive portal most of the times before a user has an opportunity to even enter a web site URL, in which case redirecting to your own (or a different) website makes sense.