Red Tomax power tables contain the power definition cast time. That's not the same thing, in a couple different ways, but it would take some time to fully explain the difference. The short answer is that the game has a powers system and an animation system that are mostly independent. But both affect the player in terms of when they can do something. The powers system has a say in how long you must wait after you activate a power before you can activate another one. The animation system has a say in when your character avatar is doing something you are not allowed to interrupt, which includes activating another power.
Because what the powers do numerically and what the animation and visual effects engine does graphically are not exactly the same thing and are not tightly coupled, what you see and what you do aren't always congruent. So in particular when someone asks what how long a power animates for, the context of that question is significant. Are they more interested in the visual aspect or the combat mechanics aspect? And besides that, it is still a complicated question to answer.
Complicated enough that even though I worked out the most detailed description of how this works back in the day, it was still the case that no one, not I and not even the devs, could *precisely* describe how this works in a way that gave 100% accurate answers to the question "how long does this take?" It is not that the game was weird or glitchy, but rather that in a pseudo-real time system like City of Heroes technically is, there are always complex corner cases and timing trivia to deal with.
To this day I haven't played a game where this situation is nearly as complex, not because those other games somehow magically avoid these problems but because most MMOs use regulatory mechanisms like global cooldowns and timing interlocks that slow combat down into very predictable (and thus easy to balance) timing. City of Heroes didn't do that: it let players do things more or less as fast as they could happen. This is a balance-nightmare, but it is also at the heart of the faster paced combat (for a traditional MMO) City of Heroes supported.