If you have Subscription plan set for your product, then it should be fine. You can make a test payment using this guide https://s-plugins.com/complete-test-transaction-using-stripe-payments-plugin/ and then have a look at your Stripe Dashboard to see if new test subscription is there.
And how do the customers know that it is a subscription?
You can add some description on the page that this is a subscription. Also, you can make a note in product short description that this is a subscription. The note will be displayed in payment popup: