What is the likelyhood of cesium to be detected in tap water?

Cesium is chemically similar to sodium - it is in the same column of the periodic table. So a charcoal filter won't do much to remove Cs - what you would need would be an ion exchange filter to remove Cs. Depending on the type of exchange filter, it would replace Cs with either sodium or H+ ion. That said, the incremental threat posed by the Cesium activity in your tap water is trivial. You would, metaphorically speaking, reduce your likelihood of premature death more by dropping your commuting speed by 10 mph for a week. Or, more to the point, you would reduce your exposure to ionizing radiation (from radon and its daughter products) by a larger amount by installing a ventilation fan in your basement or the crawl-space under your home.