The common trick with other modules is to assign a teacher to each group and to set "separate groups" for that activity. Then each teacher will be able to see and grade only students in his/her group. Whether the activity is on the same day or not,it doesn't matter, as soon as all the group will perform the same activities at some time. (if not, probably you currently need to set up different courses)
Unfortunately, this trick doesn't seem to work with the attendance module, as teachers are able to see and possibly take the attendance (currently only if they have edit right to "yes", as the "take attendances" function does not work) also of groups to which they were not assigned.
You could possibly use an offline assigment activity for this:
The assignment could be something like: "Be present at the group meeting (or attend a chat session, or wathever is the activity). Group A will meet monday in room #1 and group B in wednesday in room #2"
Each tutor assigned to a group (even with edit right assigned to "no") will be able to grade attendance of each student of his/her group, and even of taking notes about it. If a tutor follows more than one group, you will have to assign him/her more than one identity (username/password), as one cannot be assigned to more than one group.
Piersante