I set up a 14 day free trial system with automated interval change, but Shopify Checkout still shows that the subscription will be renewed every 14 days.

The thing to know here is that Shopify Checkout isn't aware of this upcoming interval change, hence why they don't show this in the checkout. 
So a workaround for this is to edit the text which shows when the customer will be charged to something else, which will explain that they get a free trial. You can change this in Shopify admin > online store > click three dots next to your published theme > choose "edit default theme content" > find the text > edit the text > save changes.