I agree with mattb, and the notice has got nothing to do with it – as mattb has pointed out, and you say you told the tenant 2 months before.
Also, the tenant told you they were moving out because of the works, but that may not be true. We did some major works some time ago, and a tenant moved out in the middle of them. The owner then told us that we were responsible for them moving out, and I said well that’s interesting, because the tenant told me he was moving out because he was moving to Melbourne…..