Even if the builder doesn’t need insurance for jobs under $4000 their insurance for the whole company should cover them – unless they are a small, semi-professional business doing this on the cheap.
The best thing you can do if you are worried is to employ a legitimate and established builder who isn’t going to disappear in a puff of brick dust as soon as a problem appears.
That will probably cost more – but there’s your insurance.
As for the long-term damage risk, with all the work going on in your building, who’s to say which apartment’s renovation caused the problem?