The live account works with ARB (Automated Recurring Billing), but the test gateway does not. Not a big deal, because the test gateway doesn't actually give us money, but it would've been nice to know.
At any rate—everything is working fine now. For anyone who may read this in the future, as of this writing, Authorize.net has an Automated Recurring Billing menu option. From there, you can view the accounts that are set up to use ARB. I mention this, because when you see the first transaction(s), you will notice that ARB does not look like it's working—the daily reports will have an "N" next to the "Recurring Billing", signifying "no"; the ARB menu option will read "0 out of ____" charges have been made. As long as you have ARB set up with Authorize.net, you can safely disregard that. Yes, their system needs to be changed, and yes, the next payment will be automatically billed.