Shua wrote:
Rasi explains that אחר means soon after while אחרי means long after. How soon is soon? How long is long? Would you use אחרי to speak about something hundreds or thousands of years in the future?

I think what Rashi means is that אחר הדברים means immediately after, with nothing intervening, and אחרי הדברים means some time after, maybe only a few days.