All times received by the API will be in UTC timezone. Meaning you need to apply the corresponding timezone offset for start/end dates before making a request.
It seems to work by adding time after the date, which was not clear in the doc that a date is a date + time format.
start_date : Use the Activity due date where you wish to begin fetching Activities from. Insert due date in YYYY-MM-DD format. Pipedrive API v1 Reference