You're talking about batch-sparging here. Generally, the aim is to mash for 60-90 minutes at 62c-68c then top-up with sparge #1 to get the temperature upto 72c-80c, leave 10 minutes, drain to boiler then refill with batch #2 again aiming for 72c-80c, leave 10 minutes then you hopefully have your pre-boil volume. The 72c-80c 10 minute rest is to stop the conversion process of the starches into sugar.
There are other ways and running off the initial mash volume to the boiler before topping up is one as is fly-sparging but if your mash tun has the capacity to do a two step batch sparge and batch-sparging is your preference then I would go with that. I myself batch-sparge simply because it's easier and more foolproof than fly-sparging for me. Fly-sparging would without doubt give me better efficiencies but I would likely end up extracting tannins and whatnot.
Apologies for the centigrade measurements, it's what we tend to work with in the UK.