I never signed the contract. Do the terms still apply?

Often yes. A construction contract does not need a signature to bind you. If one side put terms forward and you then started work against them without objecting, a court or an adjudicator, the independent person who decides construction disputes quickly, may well find you accepted those terms by conduct, meaning by your actions rather than your signature. Where both sides kept sending competing terms back and forth, sometimes called the battle of the forms, the last set sent before work began can prevail, though it depends on what the emails and conduct show was accepted, which is why the final message often matters more than the first. And if no complete set of terms was ever agreed, there can still be a contract on the basics, with the Scheme for Construction Contracts, the fallback rules the law reads in, filling the gaps on payment and dispute resolution. Assuming no signature means no obligations is the dangerous position: it usually just means nobody is certain which obligations apply, and that uncertainty surfaces at the worst moment, so pin down from the paper trail what you are working under before a dispute forces the question.

Say a plastering subcontractor is emailed a set of terms on a Thursday, never signs anything, and simply turns up and starts work on the Monday. Months later a dispute blows up and they argue no terms apply because they never signed. In practice a court or adjudicator may well find they accepted those emailed terms by conduct, by starting work without objecting. If instead both sides had traded competing terms, the last set sent before work began could carry the day, depending on what the emails and conduct show was accepted. And if the terms were too incomplete to form a full contract, the Scheme's fallback rules would still fill the gaps on payment and disputes. No signature rarely means no obligations; it just means the position has to be pieced together from the paper trail, a poor place to start an argument.