CREATE TRIGGER YourTrigger
ON Data
FOR INSERT,UPDATE
AS
BEGIN

DELETE a
FROM INSERTED i
INNER JOIN Person p
ON p.ID = i.PersonID
INNER JOIN Session s
ON s.ID = i.SessionID
INNER JOIN AggregateTable a
ON a.PersonName =  p.Firstname + ' ' + p.Lastname
AND a.[Date] = s.[Date]

INSERT INTO AggregateTable (PersonName,[Date],TotalTime)
SELECT p.Firstname + ' ' + p.Lastname,
s.[Date],
CONVERT(varchar(8),DATEADD(ss,SUM(d.Secs),0),108) AS TotalTime
FROM INSERTED d
INNER JOIN Person p
ON p.ID = d.PersonID
INNER JOIN Session s
ON s.ID = d.SessionID
GROUP BY  p.Firstname + ' ' + p.Lastname,
s.[Date]

END

CREATE TRIGGER DataAfterInsertUpdate
    ON Data AFTER INSERT, UPDATE
AS
BEGIN

MERGE
    RZData AS Target
USING
    (
        SELECT
            CAST(Session.[Date] AS DATE) AS SessionDate,
            Inserted.PersonID,
            SUM(Inserted.Secs) AS Secs
        FROM 
            Inserted
        INNER JOIN
            Session
            ON Inserted.SessionID = Session.ID
        GROUP BY
            CAST(Session.[Date] AS DATE),
            Inserted.PersonID  
    ) AS Source
    ON Target.PersonID = Source.PersonID
    AND Target.[Date] = Source.SessionDate
WHEN MATCHED THEN
    UPDATE
        SET 
            Target.Mins = ((Target.Secs + Source.Secs) / 60),
            Target.Secs = ((Target.Secs + Source.Secs) % 60)
WHEN NOT MATCHED THEN
    INSERT
    (
        [Date], 
        PersonID,
        Mins,
        Secs
    )
    VALUES
    (
        Source.SessionDate,
        Source.PersonID,
        Source.Secs / 60,
        Source.Secs % 60

    );
END