I never used the TaskScheduler.au3 UDF but it should store event datetime stamps in UTC, without any offset. The task should trigger when the PC UTC clock matches that of the scheduler, period. Exactly like what @argumentum posted while I was typing.
UTC is the same for everyone everywhere on Earth and anytime.
Of course if you move your laptop from one timezone + DST rule to another area having another set of rules, without telling your PC that the local rules have changed, then the bell will ring at the wrong time.
Contrary to a laptop, a smartphone connected to a local GSM network knows when you change location and hopefully adjusts the local parameters to where you go.