No, it’s just a misconception that people can only see your twitter posts if they are following you.
Each and every person have the chance to see your tweets till your account is public.
As you put on privacy on your account by making it to private account then in that particular case a person has to follow you to see your tweets on Twitter.
Till your twitter account is public all your tweets could be viewed people on twitter and these are some different paths from where people can view them:
- Entering directly into your profile page
- Searching your username on twitter search
- By lists, hashtags or other RTs
If you are uncomfortable with people you don't know viewing your tweets I recommend you check your privacy configuration.