I am not sure how being taxed at source is handled.
This link talks about paying taxes for canton Vaud (in French).
http://www.vd.ch/themes/etat-droit-f...ger-de-canton/
It says that it is based on where you live at the end of the year, that you pay the whole of the taxes. You would be reimbursed for the taxes you paid to the other canton so that you can give it to Vaud.
I had this happen when I moved from Lausanne to Bern at the beginning of December. I had to pay for the whole year in Bern. I had to get my tax money back from Vaud and then give it to Bern. Why this couldnt be done directly by them, I dont know.
I am not taxed at source though so do not know how that works for your situation.
Your best bet might be to call and ask how source taxation is handled.