In starship combat, a successful Taunt captain action imposes penalties on opposing crew members for a period of 1d4 rounds if they "act" during the phase in which the Taunt occurs. To quote the rules (emphasis added):
If you are successful, each enemy character acting during the selected phase takes a –2 penalty to all checks for 1d4 rounds
So if the captain of Ship A Taunts Ship B at the beginning of the helm phase, before Ship B’s pilot has taken their pilot action, then the pilot of Ship B has the option to decline to take an action for that round in an effort to avoid taking the penalty for 1d4 rounds. However, the pilot must roll a piloting check that round to determine which ship moves first. This mandatory piloting check is not a starship combat action, but does it count as "acting" for the purposes of the Taunt?