Here are my personal thoughts on recomps; they are a cover up for steroid use.
Now that I have that out of the way, let's talk about the theory of a recomp. The adjustment of macros usually consists of increases in protein and fats, and decreases carbs, or vise versa, depending on where you are atm. That being said, the calories should stay the same.
All newbs in the game can lose fat and gain muscle at the same time. That first year can be pretty amazing in terms of progress and the body seems to adapt nicely. Once the "honeymoon phase" is over, however, you can no longer build muscle in a caloric deficit, or, at least, it's near impossible. Let's just say near impossible for argument's sake. The reason why is, once you reach a certain amount of lean body mass, it begins to take more and more calories to maintain. If you go in to a caloric deficit, the body will usually look for ways to "survive", and if you are holding a lot of LBM, it will likely attempt to decrease muscle mass, considering muscle mass is "expensive". Remember that the body is a very efficient machine, and larger amounts of muscle mass is not efficient to have.
So, that being said, I would simply adjust calories and macros to reach one of two goals.
1. Cut
2. Gain muscle
Trying to do both of these things makes at once while natural will lead to less than optimum results. Remember that, in a caloric deficit, the value of protein goes up, while the value of carbs actually stays the same. In a surplus, protein value is sort of moderate. So not only is not best from a calorie perspective, but it's also not always best in a macro perspective. The adjustment of macros is never a bad idea though. Try to experiment with them a little. A little more protein is usually never a bad idea. Only time it won't have an impact is in very high surpluses.
Hope this was not too long winded and it was helpful. I left out a LOT of details here to keep myself from rambling or going too far off topic.