I had similar problems with cooldown animations not showing even with the new BlizzardCC stuff disabled. There is another thread in this subforum about it.
The easiest solution I found was to just inherit from Blizzard's default cooldown frame when creating the cooldown frame for your custom addons.
In this case, change line 257 in that file you linked from
Code:
local cd = CreateFrame("Cooldown", nil, icon)
to
Code:
local cd = CreateFrame("Cooldown", nil, icon, "CooldownFrameTemplate")
and see if that fixes the problem.
There is probably a deeper reason for this issue, but since that simple inheritance fixed it for me I stopped looking.