Tried it now. Didn't work.
I have thrown in some print lines and now I am really confused:
//Set the seconds to zero
Serial.println(t);
int seconds = t % 60;
t -= seconds;
Serial.println(t);
//Finally set the selected time
setTime(t);
Serial.println(now());
Serial.println("----------");
This was the output:
62701
62700
62708
----------
62712
62700
62707
----------
62715
62700
62713
----------
62793
62760
62768
----------
62820
62820
62830
----------
It seems to add random seconds to the number. I hope this is my fault somewhere and not a bug in the library.
By the way, the number is so small because I have set the date to the 1. 1. 1970 since my clock doesn't need the date.