DIAGNOSIS Residual cleaning solution (vinegar or descaler) is stuck in the water lines or the ice-making assembly. The taste is being imparted to the water before it freezes.
FIX You need to do multiple rinse cycles. Fill the reservoir with fresh cold water. Run the machine, but discard the first 2-3 full batches of ice it makes. Don't taste-test until you're on the fourth batch. Run a batch, empty the basket, repeat.
IF THAT DIDN'T WORK If the plastic taste persists, it might be from the newness of the parts or a biofilm. Make a baking soda solution (a tablespoon dissolved in the reservoir of warm water), let it sit in the system for 15 minutes, then run it through a cycle. Follow with several clear water rinse cycles. Baking soda is better at neutralizing odors than vinegar.
HEADS UP Never use bleach or harsh chemical cleaners. They can degrade the food-safe plastic and leave a permanent taste. Stick to vinegar or citric acid for descaling.