You have used two terms Condition and Maturity, you have to be very careful using them interchangeably.
In brewing books (especially UK books) you will see that they refer to packaged beer coming into condition.
By packaged we are talking about bottle, keg or cask beer all have very different requirements to be regarded as in condition which is used to mean ready to go to market.
Carbonation is a part, admittedly a vital part of the beer being in condition. But its far from the only criteria.
Lets look at say a Hefeweizen, it might require 9g/L of carbonation but only takes a week or two to taste best. Means you want to get the fizz into it pretty quickly.
At the other end say an Imperial Stout might only want 3-4g/L of CO2 but will benefit from up to a year to mature or to come into condition. The rate that you make the fizz is pretty irrelevant in that case.
As mentioned above the temperature is an important part of the process. The fermentation that makes the fizz is just a continuation of the ferment. You don't even need to prime bottles, if you know where the beer is going to finish you could package it with the right amount of residual sugar required to make the fizz you want.
The ideal temperature to "condition" beer is the temperature you fermented it at!
Remember that yeast hates sudden changes in temperature. The smaller the package the faster the temperature will change in either direction. We take say 23L of beer out of a single temperature controlled environment, put it in small containers and shove them under the bench. First night the temperature plummets and the yeast goes to sleep and stays that way or often just limps along and takes weeks to do what it should do in days at most.
Some yeasts will continue chipping away at sugars even at very low temperatures, Lagers sure but I have has a Cider peel off a couple of points in a keg in the fridge, went from semi sweet to dry as over a couple of months.
Last point
Even once the fizz is right, the beer will still change (mature) good rule of thumb, beer will mature better cooler, but slower.
Mark