1) It appears you are working with ESRI GRIDs. You will want to change:
rasters = arcpy.ListRasters("*", "TIF")
to:
rasters = arcpy.ListRasters("*", "GRID")
2) The rasters are saving to your env.workspace. You set this to your rasterWorkspace variable. So, the rasters should save here once once you make the change mentioned above.
Also, it's helpful to add print statements throughout your code. For example:
for shapefile in shapefiles:
shapefileName = shapefile.split(".")[0]
print shapefileName
for raster in rasters:
rasterName = raster.split(".")[0]
print rasterName
if rasterName == shapefileName:
outZonalStats = ZonalStatistics(shapefileName, "value", rasterName, "SUM", "DATA")
print "Saving raster"
outZonalStats.save("zoneStats_" + shapefileName)