First of all int cannot store fractions, so you will probably want to use float or double instead.
But why are you dividing by 1000. $seconds_diff consists of a seconds, so dividing by 60 will give you fraction of a minute.
For example: If $seconds_diff is a value of 13 [seconds]:
$duration_in_minutes = round($seconds_diff / 60, 2);
$duration_in_milliseconds = $seconds_diff * 1000;
If it is your goal to use milliseconds then use microtime() instead of time():
http://php.net/manual/de/function.microtime.php
Recommendation
Just measure the time with microtime() and directly store the result in the database without rounding, dividing or formatting. Then later on, do the formatting when you have to output it. This will give you more precise results and more freedom.
$start_time = microtime();
…
$end_time = microtime();
$duration = $end_time - $start_time; // duration in milliseconds --> save to database
When outputting, for example:
$duration = get_duration_from_database(); // pseudo function
printf('%.2f minutes', $duration / 1000 / 60);