Hi,
It's normal that the order does not appear in Akeeba Subscriptions as the order is handled in HikaShop. You should only see the subscription there.
Now could you answer my questions please ? Did you activate the recurring option in your subscription ? Is the order confirmed in HikaShop ?
If that's the case, then we'll need to see some screenshots of your options as what you're describing is correct and it must be something else: the akeeba subscription plugin's options, the paypal recurring payment method options, the product and the subscription in Akeeba Subscriptions.