Any time you are being less specific than the day itself, use “in” to indicate that the event happened at a time within the boundaries of that century, decade, year, or month.

In the 20th century…

In the late ’80s…

In 1989…

In June, 1989

When the day is known, you can say “On June 20, 1989…” or “On that day in June…”.

When the hour is known, you can say “At 3:05 pm on June 20, 1989…”.

For any of these levels, estimates or approximations would be preceded by “around” or some similar term. (“Around 1990…”, “At approximately 3 pm…”, “At 3 pm or so…”, etc.)