The Asha'man don't have any great love or respect for the White Tower but I don't think its clear that they want to wipe them out. Taim did try to stirr things up between Rand & the Aes Sedai but I think that was more about making sure that Rand would only have male channelers i.e. Asha'man he could turn to for help.

If Rand also has the option of being able to call on Aes Sedai it kept his options open and Taim's position is not quite as strong.

The Shadow could order the darkfriend Asha'man to attack the Tower but why would they want to do it at the same time of the Seanchan. At the moment the White Tower is 100% light friends and most of the Seanchan military are likewise opposed to the Shadow.

It would make a lot more sense for the Shadow to let the two forces of the light attack each other and then send in dark Asha'man to attack the survivors of both groups. Going in at the same time is likely to result in a lot highter casualties for the dark friend Asha'man and the Shadow is not going to waste those valuable resources.