Here is the answer:
for (var i = 0; i < eventArray.length; i++) {
startDate = eventArray[i].start.date || eventArray[i].start.dateTime;
endDate = eventArray[i].end.date || eventArray[i].end.dateTime;
summary = eventArray[i].summary;
description = eventArray[i].description;
htmlLink = eventArray[i].htmlLink;
event_location = eventArray[i].location;
/*For safari, we have to take out date, month and year individually, as I was getting date in startDate, so I parted it and went ahead */
var parts = startDate.match(/(\d+)/g);
eventStartDate = new Date(parts[0], parts[1]-1, parts[2])
/** Here was Invalid date issue for Safari which I was facing earlier eventStartDate = new Date(startDate); **/