Yes, you hit on the snag that Adobe almost solely is responsible for making. See they made it easy, but they also made it hard to understand whats going on at the same time. Now everybody does this but you cant do any basic arithmetic in any imaging application anymore.
http://www.teamten.com/lawrence/graphics/premultiplication/
What am i missing here?
Just about everything about how images and maya really work, unfortunately.
So now if you say the alpha is premultiplied the equation ends up like that: 0 color * 0 Alpha = 0 (transpar
Oops i had typo in the formula. sorry. Its color - alpha*color + alpha*layer below (fixed in source)
But thats why i stored a black and white alpha channel in the tiff file.
No you used photoshop and assumed layering is somehow fundamenta, well yeah sure but what if you want to do something even more fundamental such as addition? Surface shader is a do it yourself function, but that means you must DO EVERYTHING YOURSELF, including computing the alpha mask on everything. That means control but also responsibility
I also deleted every color information where it should be transparent.
Each pixel in your image HAS 4 values. Theres no such thing as a pixel with no color. Even pxels you think as having no color, do have a color. There quite literary is no such thing as apixel in image that has no color information, that is impossible. Your transparent pixels are white, simple enough.
See thast not what alpha is about. Alpha is just a metric on how much to show the layerand how much to delete of the intensity of layer below.
And by the way if you sue photoshop, then you can never really know what particular color phostoshop chose to flood this time. Mostly its white but some formats also are black. But reload this tiff into PS and behold it is white (assuming you didnt use CS, CS2 before they fixed the functionality of auto alpha loading back, because then PS will never let you know unless you go really tech).
Suggest you to Re-evaluate everything you think you know about images. 
I discovered this! If i plug my tiff file in a lambert shader and then plug the lambert shader in a surface
shader the puicture will be rendered right.
Not quite you get a white fringe.
Lol, yes becasue it actually does multiply the colors to black. You could have put the color onto the lamberts ambient channel and kill color too. But also not quite you get a white fringe.
In any case theres a much easy way to do this with the surface shader, and thats simply to do it how shading is actually done.
Connect Out Transparency to Out Matte Opaciy
Connect Out Alpha to Out Transparency R G and B
Now the color part follows
Simple arithemtic is if premutiplied by black:
Connect your image Out Color to a Out Color
Premultiplied by white on the otherhand reduces to:
Connect your image Out Color to a plus minus average node input [0]
Connect Out Alpha to same plus minus average node input [1] r g and b
Connect output 3d to Out Color
set mode to minus, Now you have the 100% correct composition
Other premultiplication colors are possible but have a bit more to implement