The date calculations shouldn't be affected by the system timezone because all internal calculations are done using the UTC base of the dates.
It is however affected by the format you use to specify the input date values (such as startDate). It will accept date strings that specify a timezone but these dates will be normalized to UTC by default.
Example:
ISO 8601 date string without TZ:
> new DayPilot.Date("2019-01-01T00:00:00")
DayPilot.DateĀ {value: "2019-01-01T00:00:00"}
ISO 8601 date string with TZ:
> new DayPilot.Date("2019-01-01T00:00:00+02:00")
DayPilot.DateĀ {value: "2018-12-31T22:00:00"}
If you have a Date value you need to convert it to DayPilot.Date explicitly like this to read the local date/time value.
dp.startDate = new DayPilot.Date(yourDate, true);
Otherwise it will use the UTC base:
dp.startDate = new DayPilot.Date(yourDate);
See also:
https://api.daypilot.org/daypilot-date-class/
Please let me know if it didn't help.