Final answer:
The phlebotomist should wash the site with a disinfectant and report the incident to the immediate supervisor.
Step-by-step explanation:
The phlebotomist's immediate course of action should be to wash the site with a disinfectant for a minimum of 30 seconds. This is important to reduce the risk of infection from potential bloodborne pathogens such as HIV, HBV, and HCV. After washing, the phlebotomist should also report the incident to the immediate supervisor. Following these steps can help minimize the risk of transmission and ensure proper reporting and follow-up.