I found the answer here: https://stackoverflow.com/a/23030127/1011766
Because fswatch is a long-running process, I had to use sed's -u flag to unbuffer the stream.
-u, --unbuffered
load minimal amounts of data from the input files and flush the output buffers more often
This simple fix did it:
fswatch -xr mysitedir | sed -un '/Updated$/p' | xargs -L1 -I {} echo {}