edit was to clear up the math, because 1.4 attack speed means you attack about every .7s, but anyway, the fact that you are pointing out my edits as if they are an attempt to discredit you says something about that '1up' game you aren't playing.
I'm pointing them out because you edited it after I responded. If you are having a conversation with somebody and they respond to you have the courtesy to at least notate what you edited if you are going to edit a post after it has been responded to. While I'm not saying you did, some people choose to use this mechanic to say things then go back and edit them as a means of trolling.
With that said. You aren't quite understanding how POB works. Yes it's a dot, but it's a dot that stacks.
Each "round of damage" adds to each other up to 5 I believe. Therefor over the course of casting it the total damage being done increase by EACH round of dots that stack ontop of each other. Hence the "increase of damage over time".
If you sustain the spell it will do ALL 5 dots at the same dropping the oldest, adding the newest keeping it's maxing damage once you have all 5 ticking in rotation. However a single attack (hit and run) will not do as much damage as if you waited for the full 5 tick to hit and run the course of it's lifespan
It's something that is very easily noticed by simply watching the rate of decrease in life as you use the spell. You can watch as the longer it is casted (up to 5 ticks) will increase the rate at which life is decreased from your target.
Increasing your attack speed will decrease the time between the ticks (at least I've noticed this and other have spoken to it, and I believe you agree with). Which will allow you to ramp up from 1 dot to 5 stackable dots quicker.
So yes it does ramp up. As your first attack is only the first of 5 stack-able dots that damage over the course of I believe 5 seconds each could be 3 as you say. I haven't gone out of my way to time it with more then just verbal count down.