When you cancel your Premium subscription, you won't be charged on your next billing date - and you'll be able to use Premium until that date (so it won't revert to free immediately). After that date, you'll be reverted to the free ad-supported version of Spotify.
In your case, since you've already renewed your subscription on 5/29/19, if you cancel it today - you'll still have access to Premium until 6/29/19, and then you'll revert to the free service. No worries, you won't be wasting any money and you won't be charged on your next billing date when you cancel.
There is also some additional information on canceling your Premium subscription here.
I hope this helps! Let me know if you have any more questions 🙂
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