Step Temperature and Time?

This is my first post and second batch of beer, so don't rip my head off if I say something wrong. I recently made an ale recipe (all grain) I found in popular mechanics. It was my first batch and it turned out terrible. I skipped the whole batch sparge, and just added in water. Lol anyway I am planning on another attempt (but in smaller amounts in-case of failure) and I'm making a mash tun this time. I want to make a Hoegaarden clone and because of the wheat content I will need to do a double infusion. I have step temp. and times, however I don't fully understand the instructions. This is what it says:
(Protein Rest) Add 4.50 qt. of water at 132.1 F 122.0 F for 30 min
(Saccrification) Add 4.00 qt. of water at 208.0 F 154.0 F for 30 min
(Mash Out) Add 3.50 qt. of water at 211.0 F 168.0 F for 10 min.
I understand that I need the different steps for best results. What I'm asking is do I add water at 131 to the grain in my mash tun and allow it to cool to 122, then cover it for 30 min and so on? This is a first for me and I would greatly appreciate an explanation. Thanks a lot guys!

Ok I think i see what you are asking. If you have your grain at room temperature and add 4.5qt of water at 132. the resulting temperature of the mixture should be at 122. you will then cover the mash tun and wait 30 min. then add 4 qt of 208 degree water to get the whole thing to 154 (this is where the magic happens.) then the mash out step. I think your hang up is not realizing the cool grain and hot water will create a mixture that will be at a temperature between the two. Also what size batch is this? if its 5 gallons you will absolutely need to sparge or you will have another failed batch.

I was confused about the cooler grains mixed with the hotter water. I was not sure, but you have confirmed my thoughts. Thanks! And the next batch size I wanted to make around 2.5 gal. I planned on doing a batch sparge with the mash tun I'm going to make. I won't make the mistake of skimping on the sparge again. I saw a few articles saying a batch sparge works well. If I'm correct they said add in your sparge water (after you recirculate the first few quarts) then stir and let it soak and settle for about 15 min.

Yep that the general concept.

Nice. Thanks for your help