Now I need to know, do my members just login to with their Yahoo id and password, ...
No, they do not use their Yahoo ID or password.
The transfer agent did not have access to any of their Yahoo account information, just the info in your Y!Group's Manage Members list.
?
or will they need to create a new one for IO groups?
?
As Bruce said, they'll only need to log in to Groups.io if they want to access the web features. Files, Photos, etc. For just reading and posting by email there's nothing they need to do.
However if they do want to log in to Groups.io, their "ID" is their email address - the one in your group's Members list. Then follow the instructions to create a password or to log in without one.