With batch sparging I don't think it matters how you add it. Just add it and stir well. Your grain temp should be 170F at this point. Give it 10 to 15 minutes to rest then recirculate as described and drain.
Excellent link posted above.
I think the recommended method is to have both running be the same size. So if you expect 7.5gal total then each draining should be 3.75gal. So you need to add 1.25gal to your mash and stir before starting your first drain. Then add 3.75gal for the second runnings, stirring again.
The other possibility is to do three runnings of 2.5gal each. This means you would drain your mash water for 2.5gal. Then add 2.5gal and stir, wait 10-15 then drain. Finally add the last 2.5gal, stir, wait, and drain.
I wonder if you get better efficiency if you sparge in three runnings or in just two?