How do I stop seconds displaying 60 before going back to 0

I'm trying to display the time in the player's UI but I can't seem to stop the seconds displaying 60 before it goes back to 0. I thought it would do everything in the if statement first before displaying anything, but that doesn't seem to be the case. Here is my code:

private void Update() {

    seconds += timeMultiplier * Time.deltaTime;

    if (seconds >= 60) {
        seconds -= 60;
        minutes += 1;
    } else if (minutes >= 60) {
        minutes -= 60;
        hours += 1;
    } else if (hours >= 24) {
        hours -= 24;
        days += 1;
    } else if (days >= 7) {
        days -= 7;
        weeks += 1;
    } else if (weeks >= 52.17857f) {
        weeks -= 52.17857f;
        years += 1;
    }

}

public string DisplayTimeInformation() {
    StringBuilder builder = new StringBuilder();

    builder.Append(hours.ToString("#00")).Append(":").Append(minutes.ToString("#00"));

    if (displaySeconds) {
        builder.Append(":").Append(seconds.ToString("#00")).Append(" ");
    } else {
        builder.Append(" ");
    }

    return builder.ToString();
}

I tried using a second displayedSeconds that is the same as the normal seconds variable and clamping it to 59, and even though it was technically still accurate, it would linger on 59 for a bit and then speed up from 00 to 01 before returning to normal which just doesn't look nice.

There is no need to calculate all of those time properties. It's much easier to record the time something started:

var startedOn = DateTime.Now;

and then every time you display the duration do:

var difference = DateTime.Now - startedOn;

Which gives you a nice TimeSpan object that you can display easily:

var timeInString = difference.ToString(@"hh\:mm\:ss");

See here for how you can specify your own format string.

It is more easy to use TimeSpan for calculations. You can use this class for obtaining hours, minutes and seconds depens on deltaTime and timeMultiplier:

 public class Timer
    {
        public int Seconds => timeSpan.Seconds;

        public int Minutes => timeSpan.Minutes;

        public int Hours => timeSpan.Hours;

        private TimeSpan timeSpan;

        public void Update(double timeMultiplier, double deltaTime)
        {
            timeSpan = timeSpan.Add(TimeSpan.FromSeconds(timeMultiplier * deltaTime));

            Console.WriteLine(timeSpan.ToString(@"hh\:mm\:ss"));
        }
    }