As others have enlightened me, the delay start is just that, a delayed start, meaning, it will delay the turn on of the LM2596. However, it seems the problem I am having is not that, and needs to be fixed using some kind of a Soft Start circuit on the output of the LM2596. This is where I am confused, but happy to learn.
I am trying to search for 'LM2596 Soft Start' circuit schematics, but I'm running out of luck. I am a visual person, and I need to see stuff drawn in order to understand it.