What are the conditions you've set for the automation? It will only go to 'old' subscribers if you've set some sort of action that includes them. For example if you've set the sequence to trigger when you add Tag A to people, but then you realize you want Tag A to be on everyone, it will go to everyone (unless the old subscribers have been sent this email before, then they should never get a duplicate email).
If you've just got it to send after they enter through a form/landing page, you're all good. Only people who go through stuff after you've put it on active will get it. It won't retroactively add previous subscribers. Basically, don't add whatever trigger you've set on the old subscribers and you should be good.