Without even checking with the computer analysis, I could see the value behind 25...R4c7. I think the "insight" is much more simple than you may think; I think it is just simply that White wants to play Ra7 to infiltrate and attack the b7 Bishop. The Rook retreat just covers this before it can be played so the b7 Bishop doesn't have to be tied down. I don't know if there is such "rule of thumb" when to retreat doubled Rooks unfortunately.
The bright side though is that the concept is a really simple one taking another form here. The "concept" at play (at least how I see it, but a GM may prove my thinking completely wrong 
) here is "piece activity" that beginners are taught! Of course, it is a not-so-obvious example though. Just stepping back from the game and looking at only the Rook's position on c4 will reveal that it looks a bit boxed in, or even clumsy. If the Rook isn't ideal on c4, then where could it move to? Back to c7 is a nice improvement; also note how the "retreat" doesn't take any pressure off of the backwards c3 pawn. The doubled Rooks are still eyeing c3 and White can't really go for c3-c4 anyway due to ...dxc4 as well as the Rooks (since the Rook on c7 would also protect b7). Keep in mind that this "stepping back" perspective I gave is great in many contexts to find positional motifs, but it doesn't account for tactical problems: with that said, it is good to step back and see the positional themes at play and then decide if there are any tactical reasons the idea isn't so great.
In short, I believe that the retreat is simply recommended because the c4 Rook wasn't actively doing much there and back on c7 it serves another purpose (anticipating White's Ra7 soon).
I just played a game where I had my two rook in a battery pointed at my opponent's backwards pawn.
I was Black. After White's move 24. Ra1, the computer suggests 24. ... Rac8 and then 25. Rfc1 R4c7.
Can anyone give some insight into why the computer likes this rook retreat (25. ... R4c7)? Specifically it would be nice to have a rule of thumb or some general positional idea to learn from.
Thanks for your input