Final answer:
The phlebotomist should request that the patient release the fist after inserting the needle.
Step-by-step explanation:
During the routine venipuncture, the phlebotomist should request that the patient "release the fist" after inserting the needle.
When performing a venipuncture, the phlebotomist first applies a tourniquet to the patient's arm to help locate a suitable vein. Then, they insert the needle into the vein to collect the blood sample. Once the needle is successfully inserted, the phlebotomist asks the patient to release their fist, which helps ensure a steady blood flow during the collection process.