It would appear from your numbers that cooldowns are capped at a 40% decrease with some sort of rounding.

I know little about the actual workings of cooldowns however: 

Did you time the cooldowns yourself or use the games display?
Can cooldowns be 6.2 seconds etc but display as just 6?

I dont have the favor to get the -cooldown item. However do you think you could run some tests against an easy bot and get the numbers for some other DGs.

Use game settings starting DG on level 20 and filthy rich, play a single easy bot.

There are very few items in the game that increase Evasion, but that is capped at 30%, so capping cooldown isn't completely unlikely. What if they add more cooldown items later, they don't want it to be possible to get items for 0 cool down. 40% sounds like a fair cap if it exists.

It is possible that they don't stack how you are thinking. I don't know how it works for sure, but this matched  up very nicely w/ your numbers.

For fire nova, -20% would be 12. -15% off of 12 is 10.2. Another -15% off 10.2 is 8.67.

If you are using the number on the skill when it is red as the "actual cooldown" it would round up to 9 in this case, but only stay like that for .67 seconds.

I only did the math for a few, but it seems right.

Just looked it up, there is indeed a cap however it appears to be at 60% Reduction.

Found in \lua\sim\BuffAffects.lua:

function Cooldown( unit, buffName )
    local val = BuffCalculate(unit, buffName, 'Cooldown', 1)
    if val < 0.4 then
        val = 0.4
    end
    unit.Sync.CooldownMod = val
end

While immediately it may seem like a 40% Cap. The variable 'val' is calculated by 1 * (1 + Multiples), so a 60% reduction is {Mult = -0.60}, so 1 * (1 + -0.6) = 1 * (0.4) = 0.4, anything higher will be less than 0.4, and be capped at 0.4.

All percentage gains in this game are added rather than done sequentially, so -15%, -15% and -20% should be -50%. Also from what I can tell this should be above the cap, though it is late so my math might be backwards and it is 40%. Either way, if the tooltip says it should be 7 and it's 9, that is a bug regardless. Either the cooldown should be 7 or the tooltip should say 9, it's a bug either way.

From what I can tell this Cooldown function which applies this cap is performed on the actual Cooldown calulations, but is not performed on the calulation done to display the cooldown in the tooltip. This would insinuate that the tooltip is wrong and that whatever cooldown comes up is correct. I cannot however determine why your results seem to show a cap at 40% while the cap should be at 60%, I'm going to assume it is my horrible math, I should have a look at it in the morning

If this is true then the cap should be at a 60% reduction and since the max attainable in-game is currently 50% it should work.

But as of now the tooltips are a bit off depending on how you round the numbers, if you either round them up or down (and ring of fire is way off) and the cooldowns themselves are waaay of for all of them.

And i do agree as to the way it stacks as all other bonuses stacks in the same way, why shoulden't the cooldowns to that?

Taken from the demigod.wikia.com site:

Bonus Calculation

There are various bonuses (health, speed, regen, etc) from a variety of sources (items, abilities, auras, etc) and they can be absolute (i.e. +18) or relative (i.e. +70%). The calculation for all these bonuses is the same:
( Base + Absolute Bonus 1 + Absolute Bonus 2 + etc ) * ( 1 + Relative bonus 1 + Relative bonus 2 + etc )
Decimalize Relative Bonuses: 70% becomes 0.7
An extensive example:

• Base Mana per second: 8
• 18 Mana per Second bonus from Hungarling's Crown
• 1.92 Mana per Second bonus from all six Enhanced Attributes levels.
• 70% Mana per Second bonus from Plenor Battlecrown
• 150% Mana per Second bonus from Deathbringer

Leads to ( 8 + 18 + 1.92 ) * ( 1 + 0.7 + 1.5 ) = 89.344 Mana per Second.

According to this formula the Ring Of Fire would look like this:

Base cast 10 sec

no set reduction

15,15,20 in % reduction

would give

(1)*(1+15+15+20) = 50% reduction as there are no items thats give a set cooldown reduction (like a 2 sec reduction)