The start time is the time when the plugin was activated.
There is no option to do this nicely because the scheduled tasks are supervised by WordPress itself, not the plugin. The plugin simply installs the action that wants to execute and WordPress takes care of the rest. In your case, what you have to do is to deactivate the plugin and activate it at the time when you want the scheduled tasks to run at.
WARNING: Deactivating the plugin will delete all your settings and security logs, including the API key and hardening options. Be careful with this option because once you execute it there is no way to recover this information. You’ll need to request a new API key and re-configure all the settings.
