Autoresponder for second list doesn't start for existing subscribers

I have several lists that I manage on the same website that are aimed at people with different interests.

Each of these lists has a series of automatic newsletters that start going out over several weeks when a new subscriber is added to the list.

All is working fine when its a brand new email address.

However, I also have instances in which subscribers from one list end up opting in to another list and when that happens, they do NOT receive the series of automatic newsletters that is triggered when a subscriber joins a list.

This means they end up only getting the email broadcasts that go to the second list and not the autoresponder series.

Is there a way to fix that?

https://www.ads-software.com/plugins/wysija-newsletters/