a) You can scale the time scale. i.e. "Pretend" that the time units of the applet is minutes and not seconds. You set up the process time constants at dead time = 10, lag = 2 and process gain = 1. The optimum tuning for this is then controller gain = 0.29 and integral time = 4.73
These settings are just as valid in minutes as in seconds, as long as the time units of the process and controller are the same.
b) My applet unfortunitly also has a low limit of 2 time units, and your process has neglegible lag time. The good news is that with a dead time to lag ratio of 5, the optimum tuning is very similar than for a pure dead time process. If this is not good enough for you, you can contact me at pieters@ambio.co.za and i will help you with a better solution.