The reason for the batch sparge with two steps, is not as obvious as it seems. Beersmith is trying to even out your first and second runnings, so that each draining of the mash tun is the same volume. In addition, that first batch sparge addition will aid in getting your mash up to a mash out temperatue of 168F, which is the optimum temperature to vorlauf and drain your mash tun at.
The first batch sparge is added to the mash tun, while the original strike water is still in there. Theoretically, you'll then drain 3.49 gallons out of your mash tun. The 3.49 gallons is arrived at because you'll have water additions of 3.69 gallons and 1.22 gallons for a total water added up through the end of the second batch sparge of (3.69 + 1.22 = 4.91 gallons). The grain should absorb about 1.42 gallons of water so....(4.91 gallons of water added minus 1.42 gallons of grain absorbed water = 3.49 gallons of first runnings. (Note: I have no idea of you have mash tun dead space, etc., so my number could be off...this is just an example to let you know why it's done this way.)
Then you'll add, 3.49 gallons of your second batch sparge to the drained of first runnings grains, and you'll drain 3.49 gallons of second runnings back out, leaving you with 6.98 gallons of wort in your boil kettle.
This is what beersmith wants you to do. It's also the process that I use.
Further, you need to add the batch sparges at the correct temperatures, so that your mash tun settles at 168F, after your mash. What follows is how I do it....(from begining to end)....
Once you're done with your intitial mash and have your starches converted to sugars (about 1 hour of mash time), you'll add 1.22 gallons of water to your still full mash tun. You will not have drained it at all yet. You'll want to have that first 1.22 gallon batch sparge addition to be hot enough that the entire contents of your mash tun (grains, original strike water and the 1.22 first batch sparge settles at 168F. Unfortunately, you'd have to be at about 220F with your 1.22 gallons of water just to get to 168F.
How I handle this is, I heat my 1.22 gallons of first batch sparge water to boiling and add it. Stir it in and see where your mash temperature settles at. It will be in the low 160F range, depending on how much heat you lost during the 1 hour mash time.
Then, vorlauf and drain about a half gallon of wort out and bring it to a boil, then add it back in, stir and see where it settles at. If it's about 165F to 170F, close the lid and let it sit for about 10-15 minutes to let as much of the sugar in the wort thin down so that you can extract as much as possible. If you feel it's still too low, you can once again vorlauf a little bit out, bring it to a boil and add it back in. Try "not" to go over 170F, as you have the potential to extract tannins and get some grainy flavors or astrigency flavors. We don't want that flavor in our beer. Better to be a little low on the mash out temperature and suffer a little on efficiency, than to be too high and adversely affect the flavor. However, you'll eventually get the hang of it and will quickly get to 168F mash out temperatures!
Now you can vorlauf and slowly drain your mash tun (with the lid on, so that you don't lose heat!). Once you have the first wort in the boil kettle, then you add your second batch sparge of 3.49 gallons to the mash tun. What I do is I check the temperature of the grain in the mash tun, before I add the second batch sparge. I then calculate in my head about what temperature I need to be at with the second batch sparge to once again settle at about 168F. Once it's stirred in good and is at 168F, close the lid and let it sit for 10-15 minutes. You can put heat to the first runnings wort in your boil kettle and get it heading towards a boil, while you wait tha 10-15 minutes.
After the 10-15 minutes, vorlauf and drain your mash tun slowly into your boil kettle, adding this second runnings to the first runnings. You should have about 6.94 gallons in your boil kettle now.
I hope this helped!!