Closing iPhone SE cover does not lock the phone
The desired feature requires hardware support to be built into the device, which iPhone SE doesn’t have. In fact no iPhone support automatic screen lock with cover based cases.

However the same feature is built into modern iPad(s) (iPad 3 and later) when used with compatible cases.

This feature require presence of magnets in both the device and the case. iPhone doesn’t come with build in magnets.

Also, the website for the case in question nowhere mentions support for this feature.