I was advised by the building management company that the building insurance is not in effect on my unit because the damages to my unit fall below the per unit deductible ($10,000) on their master policy.
That wording is a bit odd, but I guess the gist of it is that the insurance maintained by the condo association/board and/or management company won't cover the damage to your unit.
I don't have my own condo insurance
Sorry, but that's beyond foolish. Do you have a mortgage on your condo? It's hard to imagine that your mortgage loan agreement (if you have one) doesn't include a requirement that you carry condo owner's coverage.
I should deal directly with contractor's insurance.
Please advise on how should I proceed and what I should reasonably expect from contractor and their insurance to take care of the damages.
You've (partially) answered your own question: you "should deal directly with [the] contractor's insurance [carrier]." I don't really understand what your question about what you "should reasonably expect" means, but the first thing to do is contact the contractor who caused the damage and ask for information about its insurance (and hope that, unlike you, the contractor carried proper insurance). Also, I don't know if NJ requires contractors to be bonded, but you probably should look into that also.
And is it possible that my building's insurance is still responsible for filing the claim for my unit?
In the abstract, virtually anything is possible, but no one can opine intelligently about the extent of "building's insurance" without reading the policy.