Welcome Email is automatically active in your constant contact setting by default. This is received by the new contact who recently joined your list through any signup method with constant contact integration.
If you're using constant contact API integration for your optin form and welcome emails are not being sent out to your subscribers, you would need to ensure the form is set to ACTION_BY_CONTACT instead of ACTION_BY _CUSTOMER. Please note that on optin element setting, you can't set ACTION_BY_CONTACT through it. You might want to speak with the constant contact support for this implementation with API integration.
Alternatively, try the custom form integration where you can add the 'ACTION_BY_CONTACT' at your form code. Please see the below link for custom form integration: