Thorough observations, but it might help you understand all your numbers if you first understand how DoTs stack. Assuming all gems are poison(so they stack), time is in seconds, and just knowing that each tick is 3 seconds apart, with the last tick often being a good chunk less than the rest, the formula works as follows:
Cast 1 gem : Damage over Time - ticks every 3s (last tick is less if duration not divisible by 3s)
As expected...1 is easy peasy! Now when you cast gems with some other poison effect on target:
Damage1 = poison damage already on target
Damage2 = poison damage on gem(this includes any bonuses normally)
Time1 = duration left on poison already on target
Time2 = duration of poison on gem(includes things like dark patience and hasten demise)
The new poison will look like:
newDamage = damage1+damage2
newTime = time1 * damage1 / (damage1 + damage2) + time2 * damage2 / (damage1+damage2)
newDamage over newTime is your new poison! newTime can also be slightly simplified to:
newTime = (time1 * damage1 + time2 * damage2) / (damage1+damage2)
So for a quick example, lets say you cast 2 gems, that are 30 poison over 30 seconds, to make the numbers easy, the 2nd gem will be cast 15 seconds after the first, halfway through it's duration:
First gem, is cast and starts ticking, 3 damage every 3 seconds. 15 seconds later, the 2nd gem is cast. The first gem has 15 damage left over 15 seconds. So we get:
Damage1 = 15
Time1 = 15
Damage2 = 30
TIme2 = 30
So the formula is:
newDamage = 15 + 30 = 45
newTime = 15 * 15 / (15 + 30) + 30 * 30 / (15+30) = 5+20 = 25
Giving us a new poison tick of 45 over 25 seconds, which will tick for 5.4 every 3 seconds...or in game, you will see 5 5 6 5 6...etc...to account for the rounding.
The way they work is that the stronger DoT(dps wise) has a bigger pull on duration of the new DoT effect. If you cast a higher DPS DoT after the same DoT is already applied, the total length will shorten if the higher DPS DoT has a shorter length than the one remaining on the target, or will lengthen if the higher DPS DoT has a longer length than the time remaining(will still be shorter than the newest DoT cast, but longer than what was left on the target).
In the case of the rogue CA, I have not tested it significantly, but I do have a low lvl rogue that I fooled around with a little bit. The DoT on the CA is much faster(shorter in length, aka, higher DPS than most poisons you will be casting) and so shortens the length of any poison gems quite drastically.
The DK's disease CA works very much the same...not sure how the magicians burn CA would affect burns, as they are very fast DoTs already. It would definitely increase the speed of an archers flameshot or casters burning soul procs though!
So basically, what you are seeing should be expected, casting your CA after a poison gem, would increase it's speed by a chunk, and then having a capped Rogue cast their CA after that, being a even higher DPS poison, would hasten the DoT significantly again, resulting in a shorter duration, giving the illusion that it does more damage, where as the CAs are actually "linear" in the amount of damage they do.
To test your multiplicative theory, there are 2 things you should do:
First, pick a poison gem. Cast it on a target, and IMMEDIATELY hit your rogue CA. Add up the damage from the gem AND your CA. Write it down.
Second, using the same gem, cast it on a target. Wait until only 2-3 ticks of the gem are left, then cast your rogue CA. Add up the damage from the gem AND your CA again. Make sure to start from the very first tick...also make sure you don't level anything that affects DoT damage/time/etc.
If they are the same, everything is linear, and no problems exist, it is just a matter of when you use the CA and how big the pull on duration is

You could also do this with a 2nd rogue in the fight also, just do 2 CAs quickly, or 2 CAs near the end of the poison, or one at the start and one at the end...to vary what's left on the initial poison. Just make sure you keep everything the same! Happy testing!