Can a welcome email automation series get triggered when a contact either subscribes to the related list through the API or is added manually/imported? Or does it get triggered only by web forms?

Mailercloud allows you to set email automation workflows for multiple actions taken by the contacts whether they have just joined a particular contact list through API, manually, or through webforms.

You can set a welcome email automation series to automatically trigger as soon as a contact subscribes to a particular list through API or you have added or imported that contact manually. Similarly, you can also set a welcome email automation series to trigger automatically when a contact submits a web form and gets added to a contact list.