Traditional masonry chimneys were designed and sized to vent very hot flue gases from old coal, wood burning, or low efficiency gas furnaces. Chimneys are designed to handle the heat and ash from these old heating plants. Once these are removed, your flue may be too large for the orphaned water heater.
In some cases, this can create condensation problems inside masonry chimneys. The water heater does not produce nearly the high temperature exhaust as the old furnace did. If the chimney is too cold, this can condense the water vapor in the exhaust. Sometimes this condensation is acidic and could deteriorate the masonry inside the chimney leading to problems down the road. More importantly, if the air is cold enough, the exhaust from the water heater may not be enough to completely draft out of the house. This could allow some carbon monoxide back into your house which can be dangerous.
The furnace installer should verify the installation is properly sized. There are products on the market including flexible stainless steel pipes that can be snaked down your chimney and attached directly to the water heater exhaust. This pipe also has a vent cap to cover the old chimney flue. Recommend talking with a HVAC contractor to get an understanding of the work that may be performed.