Aggressive only at certain times

[JelleyCharms]

I have two staffordshire bull terriers. They are the most loving breed i have ever encountered and the bad press they get is only through their owners not training them well.
The eldest, Babe (4years), has developed a bit of an attitude recently towards Max (3years). About two months ago when they were on a walk he attacked Max for no obvious reason. We have never experienced any behaviour like this from him before. The thing we don't understand is that it will only happen either when we are putting their leads on to take them for a walk, on the actual walk or just after their walk when we get in the house.
We know the warning signs now, Babes ears will go up, his tail down and he will look at Max in such a focused way. If Max spots this he freezes, ears down tail down and look back. This is when the start growling. If they are close enough they start fighting but we don't let them close enough for that.
It's always Babe that starts the aggression.
When they are 'winding down' from their growling match Babe doesn't even look at Max and avoids him like the plague by walking on the other side of me and speeding up when he goes by him. Max is terrified of him in these moments, shaking and hiding from him so we separate them.
We had them both castrated because of this (on the 6th of may)
Their attitudes around the house greatly improved when they had fully recovered, they are more obedient and playful (with us and each other) like they were before all this started.
We took them for a walk around the block today and kept them apart, Max being walked 15 feet ahead of Babe, the whole time there was no hostility but babe had his eyes on Max. As soon as we get into the house and Max see's Babe watching him they start growling.
I took babe out of the room and now I'm on here hoping to find a solution.
I know the testosterone is still in their bodies but I am hoping to get some tips on stopping this.
When they aren't going for a walk they are playful and loving with each other. When the harness is on its like Babe has a problem with Max that he wants to hash out.
I don't know what to do.
Does anyone have any advice?

Neither has any problems with strange dogs or people.

[Mattie]

Can you give us a run down on their day please? Include food, exercise and training. We need more information on them.

You do have Staffies which are very active dogs, my Staffy boy will come in from a really good run in the field and start to wind up my other dogs, I don't allow this, I always stop him which often isn't easy to do.

As you know the triggers, until we have more information continue to manage them at these times.