Yes you do need to twist the wires together! Splices must last through years of service. All that time the loads connected to the circuit are going on and off with accompanying heating and cooling, expansion and contraction of the wires. Splices will loosen to some degree in any case, through cold-flow of the metals involved, particularly with aluminum wires. If a connection becomes loose, the resistance of that connection increases. The greater resistance causes greater heat as current flows through it. The increased heat causes more expansion and contraction, further loosening the splice, causing more heat.... You see where this is going? The same is true of screw-terminal connections.
Copper wire is pretty forgiving, and you may see manufacturers claims that their wire connectors don't require twisting of the wires before putting on the connector, but don't you believe it. Make sure that any splices in your installation are firmly connected and would maintain a good connection even if the wire connector were to fall right off. A good electrician will make good splices and will routinely check the connections in any outlet boxes and in your electrical panel as they are opened in the course of the job.