It takes more energy to get from room temperature to hot drink temperature than it does to get from room temperature to cold drink temperature, so given the same thermal transfer rate, heating a drink will take longer to begin with.
Peltiers are pretty cool things. The difference between performance in heating and cooling mode likely has to do with several factors. Peltiers have fairly strongly defined optimal operating currents.
At too low a current, the thermal conduction losses of the peltier will dominate, determined by thermal conductivity and temperature differential along with convection as the interior grid of the peltier is likely not insulated.
At too high a current, the heat the peltier produces due to \$I^2R\$ losses through the little bismuth cubes will dominate.
Used as a cooling element, a peltier is a relatively inferior device in terms of efficiency but gets used because of the lack of moving parts, tiny form factor and electrical versatility.
Look at the way it operates in cooling mode. The heat is pumped out of the cold side of the peltier and into the hot side heatsink. The cooler you keep the hot side of the peltier, the better your efficiency will be. The hotter the heat sink gets, the more difference there will be between its temperature and ambient, and the more heat will be shed into a given volume of air. Note that all losses in the system will contribute to higher heatsink temperature. In this mode there is great value to moving air across the heatsink.
Used as a heating element, a peltier has the very special property of offering better than 100% electrical heating efficiency. You don't have to pay for all of the watts of heat with watts of electricity, but it does have to come from somewhere. I'm guessing this is where they've gone with having the device work slower in heating mode. They are avoiding the efficiency losses with using the fan (temperature differential between heatsink and ambient will be smaller in heating mode than in cooling mode and all thermal losses in the system will decrease the temperature differential and therefore decrease the value of using the fan. With a resistive heating element added, you would be able to trade off efficiency to heat the liquid more quickly.
As a final thought, in heating mode, the colder the cold side becomes, the greater the temperature differential over the peltier becomes without the liquid inside the device having to change temperature at all. The total heating ability of the peltier alone is limited to its own losses plus available external thermal energy. They are not incredibly durable devices, being composed of hard ceramic and somewhat brittle metal cubes and they are not immune to the thermal stresses from the differentials they create over themselves. The current the device operates at in heating mode may minimize these stresses, and using a resistive heater would allow the stresses to be minimized by having the heat that otherwise must be produced by losses that could be stressing the peltier produced elsewhere. On the other hand if the heatsink was shielded, you could attempt to drive it far enough below ambient to make using the fan worthwhile to speed up a portion of the heating sequence at a still-higher-than-100% electrical efficiency at risk of stressing the peltier. If you are going to use high temperature differentials, good practice is to cut grooves partway through the ceramic plates in a grid so that if the plate cracks it will crack along these lines. The grooves should be aligned between bismuth cubes and as much as possible not cross copper plates on the side being cut.