Well, in my theory, the 4 after 3 makes sense. If 3 is running, the ways to supply 4 are short. Shorter than going for the 2.
"Inboards first" means "initially first" then.

I can't say anything about the C130, I don't own it.
But, as said, some aircraft require a certain sequence because of the equipment attached to certain engines only. I don't know about the C130 but there are other birds around that need their utility hydraulics stuff or brake circuits to be powered first, so the external crew can disconnect and the plane gets self-sustaining.

All APU driven ones are self-sustaining of course (if they use their APU), birds like this 707 or a Concorde are not and you don't want to have them on the ramp with all engines running for various reasons.
So you usually target for the self-sustaining aspect first and then push the thing off the ramp without the need to counteract the idle thrust of too much engines and without a too big danger for people and vehicles close to turning blades.

I could think of a Prop like the C130 being less "stable pressure" depended than the 707 and therefor the placement of the actual external air connector might no be as important as on the 707.

Thanks for your answer, Lou. Always interesting readings.

Thanks for the clearup Lou