the Activate on Blueprint Activation rollout configuration is not meant to ensure changes in your blueprint page will be reflected onto the live copy page. All it does is activate the live copy as soon as your corresponding blueprint is activated.
To achieve your requirement, I believe the push on modify configuration would be more appropriate.
If you open up push on modify on the roll-out config, you will find the following sync actions
ContentCopyAction
ContentUpdateAction
are enabled. These actions allow you to make sure that your blueprint page is copied. Hence selecting the push on modify configuration would satisfy your requirement.
Alternatively you may wish to modify the Activate on Blueprint Activation rollout configuration by adding the above sync actions to suit your needs.