DIAGNOSIS You didn't rinse the system thoroughly enough after the vinegar cleaning cycle. Vinegar and residual cleaning solution is lingering in the water lines or tank.
FIX Run multiple fresh water cycles. Fill the tank with clean, cold water, run a full ice-making cycle, and discard that entire batch of ice. Do this two or three times. Also, wipe down the inside of the ice basket and the evaporator plate with a clean, damp cloth to remove any vinegar film.
IF THAT DIDN'T WORK If a plastic taste persists, it might be from new components off-gassing (if the unit is very new) or from using a non-food-grade cleaner. Only use white vinegar or the official cleaner tablets if available.
HEADS UP Never use bleach or harsh chemicals in the cleaning cycle. They can damage plastic components and leave a permanent foul taste or even hazardous residue.