I asked:) she says that so far there is no reductions but now when I have sin I will get smaller salary because I will pay some amount of money in case of unemployment. But the main point is she doesn't know how much she will pay after reductions....
You are very lucky to have a job without SIN, you landed your job very quickly.
I am not sure on the reduction though the reply from your manager does not sound legit. check with one of the immigrant settlement agencies near you.