Understanding how to show seconds and minutes properly

I understand most watch faces do something like

setInterval(drawSeconds, 1E3);

to show the seconds and there is a queueDraw in some.

I still don't get how to syncronize seconds and minutes - and using setInterval is a bit laggy.
Example:
When I set the interval to 1 second it will be executed sometime between the beginning and ending of the second. How can I execute just at the beginning of the second of the internal clock? Is there some kind of trigger for that?