Simple past: the event started in the past, and ended in the past.
Example: I talked to my grandparents yesterday for 1 hour from 10:00 a.m. until 11:00 a.m.
The 1 hour 'talk' started in the past and ended in the past.
Present perfect is slightly different. The event started in the past, and the ending is not clear. The ending of the event can be anytime up until now.
Yesterday at 10:00 a.m. you started talking to your grandparents...
Today I ask you: "Have you talked to your grandparents?" I'm not asking if you finished talking to your grandparents, only if you have talked to them at all.
You would respond with "Yes, I have talked to them." You are saying that, at some point in the past, you started talking to them. The length of the talk isn't important, only whether you talked to them or not.
So, to answer your questions:
1) I have already talked to my grandparents today. (present perfect)
This looks good. At some point today, you started talking to your grandparents. The end of the talk isn't important-only that you talked to them, already.
2) I already talked to my grandparents today. (simple past)
The confusion here is that you use the word 'today'. Today means the entire day and is not specific. It would be better to say: "I already talked to my grandparents this morning."
This means that your 'talk' started this morning and ended this morning.