If you're using the script provided in DS_MultiCharacterSMSExample_2021-10-08.unitypackage (linked above), set it up like the example in that package.
If you want to start conversations when starting a scene, without using a script, you can set all of their Dialogue System Triggers to OnSaveDataApplied. Make sure to set the "Conversation" variable before loading that scene. Set each Dialogue System Trigger's Conditions > Lua Conditions to check the value of the "Conversation" variable.
For example, say we have a button that starts/resumes a conversation with "Bob". In the conversation selection scene, set up a Dialogue System Trigger like this to set the variable and load the conversation scene, and configure the button's OnClick() to call its OnUse() method:

- sms1.png (28.43 KiB) Viewed 1937 times
In the conversation scene, set up your Dialogue System Trigger similarly to this:

- sms2.png (46.64 KiB) Viewed 1937 times
Note: This is just a suggestion. You don't have to do it this way. You can start or resume conversations however you want.