Date and Date Time fields handle Timezones in the same way as Salesforce. When you set a Date field like Start Date or End Date then the Date value does not account for timezone. Therefore someone in California could schedule a Task for Today which would show as due Yesterday for anyone on the other side on the world (e.g. New Zealand).

Date/Time fields will adjust for Time Zone using the Time Zone identified on your Salesforce User record.

What happens if my device Timezone differs to my Salesforce User Timezone?

Good question! When your Salesforce User record differs to your computer timezone (if you are temporarily in a different timezone) then Precursive OBX will show a warning message explaining that some labels that show dates relatively (e.g. Today/Tomorrow), or where Tasks are grouped by relative dates may appear incorrect. This is because Precursive OBX uses your Salesforce User timezone and NOT your computer timezone.