Here is a trigger on Task that I wrote, that will update the Contacts last person worked field every time a new task is inserted. You probably want to write a similar trigger for the Event obejct too, but I believe you can edit this code to do that.

trigger lastPersonWorkedFromTask on Task(after insert)
{
	// set up lists you will need
	List<Contact> consToUpdate = new List<Contact>();
	Map<Id, Task> taskMap = new Map<Id, Task>();
	
	// go through the list of tasks that were inserted
	for (Task t: Trigger.New)
	{
		// if they are related to a contact, add the contact id (whoID) and their values to a map
		if (t.WhoId  != null)
		{
			taskMap.put(t.WhoId, t);
		}
	}
	
	// if the map isnt empty
	if (taskMap.size() > 0)
	{
		// get all of the contacts related to the tasks
		consToUpdate = [SELECT Id, Last_Person_Worked__c FROM Contact WHERE Id IN: taskMap.keySet()];
		// go through the list for each contact
		for (Contact c: consToUpdate)
		{
			// set the last person worked field to the owner of the task
			c.Last_Person_Worked__c = taskMap.get(c.Id).OwnerId;
		}
		
		// if the list of contacts isnt empty, update them
		if (consToUpdate.size() > 0)
		{
			update consToUpdate;
		}
	}
}

 I hope this helps!