my expire subscribers are automatic renewed by zima system.
Thanks for reaching out.
Yes the auto-renew is the expected behaviour of the system.
If you want to stop the auto-renew, you can do that by setting your service price > 0. You can do that from the managers page by editing the assigned service plan retail price to a number > 0.
You can find it in this post FAQ 3:
Further notes 
The renew function (and auto-renew) will be later renamed to pay. It will allow adding the payment of the subscriber to their balance. When renew time comes, it checks their balance and auto-renews, otherwise the subscription will be stopped (based on customizable settings by the admin). More details on that soon.
If you have any other questions or you’d like to discuss this topic further feel free to ask.