Pores are often blocked really deep, the exfolliator removes the top skin and exposes this sebum plug, irritating it, you get a breakout. If you use a salicilic acid astringent (used for people with acne) you'll unblock those pores. Be sure to moisterize with a non comedon forming moisteriser or you'll just plug the hole before it has time to become smaller (once the irritation is down).
I use a 2% salicilic acid product right when the breakout occurs and within a day (or two if I put it a bit to late), the small buttons disapeer and a bit of dead skin flakes off; no redness remain.
If you wait too long, there's a risk of real inflammation (acne) and then it will take some time for the redness to disapear.