Think of the soy wax liner as a sheet applied to the inside of the fiber cup body, attached using two different types of adhesives. The first adhesive will hold in high temperatures, while the second adhesive loses its bonding strength when exposed to an environment of hot coffee. The wax liner does not break down at all - one of the two adhesives connected it to the fiber body will. This allows the liner to be separated from the fiber body when recycling. So, to answer your question, the soy wax will not break down at all, meaning the taste or composition of the drink being enjoyed will not change at all.
The fiber body of the cup breaks down at the same rate as a current cup, but the liner breaks down much more rapidly than then wax liners currently used. A cup design that breaks down more rapidly would be awesome, but those cups already exist and are much too expensive to be fully adopted by industry (due to cost of production).
Firstly, the prompt was to make a cup that is reclaimable for the highest benefit, which puts a focus on recycling. The fiber material is the exact same material as the cups currently used, since any changes would significantly affect manufacturing speed and associated costs, meaning they will be more expensive and less likely to be widely-adopted. Additionally, a focus on being recyclable will limit wasted resources. Since ordinary cups break down in about a year, that time frame is sufficient if they were accidentally thrown away. Finally, the wax coating in traditional cups take much longer to biodegrade, while the soybean liner used here can decompose much faster than the fiber cup.
Secondly, as a materials engineer, I understand the information you are attempting to provide but none of it applies to this design. The fiber cup shell, which provides the structural integrity of the cup, will function just like cups currently do. Even if a hot drink or multiple hot drinks were poured into the cup, they would not fail. The only chemical reaction that occurs is one of the two adhesives that keep the soybean wax lining on the cup, which will only happen when temperatures exceed 125 degrees. The average temperature of hot coffee is 150 degrees, which does the trick in loosening the liner from the fiber cup. Again, this does not remove the liner or the liner's ability to prevent the fiber cup from being saturated, which means a user can take their time in drinking their beverage. The only difference, at all, is that the liner can be separated from the fiber cup after the beverage is finished, ensuring the cup can be easily processed at almost all recycling facilities worldwide.