Add to Campaign & couple questions - REST API specific

Hello,

I'm trying to replicate the closest thing to the "Add to Campaign" MSI feature in Dynamics CRM via the REST API. We don't plan to use the MSI feature from Marketo.

It looks like one way to accomplish this is to have a Smart Campaign set with a SmartList containing a "Member of List" filter with a list created specifically for that campaign. Then in response to someone requesting we add a lead to a campaign, I would then add them to that list. So on next run of the campaign, that lead would be in "Qualified People" for that campaign and run the flows from the campaign on that lead. 

I was unable to find any way via the API to add a Lead directly to a Smart Campaign. Is is a correct understanding that doing this directly via the API is not an option?

In the campaign configuration page, there is also a "View Campaign Members" button. Which shows Campaign Members tab and Qualified People tab. I can't figure out what results in leads being populated in the "Campaign Members" tab, but my above REST approach does seem to result in them showing up in the "Qualified People" tab. What is the "Campaign Members" tab for and what determines when leads show up there?

Please let me know if you have any other insight related to implementing this type of functionality.