The code below makes a flowSet object, then trims out columns as described in other posts at this forum. Following this, I use the spillover command to create my compensation matrix as detailed here: Help with flowCore

# open .FCS files

fcs_names <- list.files(fcspath, pattern="*.fcs", full.names=TRUE)

# make a flowSet object

fs <- read.flowSet(files = list.files(fcspath, pattern = "fcs", full = TRUE))
trim_fs<-fs[ , c(1,3, 5:15)] # get rid of Time, FSC-H, and SSC-H, columns

# Make compensation matrix from flowSet
comp <- spillover(trim_fs, unstained = "Compensation_Controls_Unstained_Control_001.fcs", fsc = "FSC-A", ssc = "SSC-A", method = "median", stain_match="regexpr", useNormFilt = T, pregate = F, plot = T)

fs_comp <- fsApply(trim_fs,function(frame){
     new_frame <- compensate(frame,comp)
     new_frame
})

Doing this generates the following compensation matrix, called `comp`. BUT - in post above, there is an additional line that I removed:

​comp <- keyword(frame)$`SPILL` 

appears. I removed it, based on Greg Finak's caveat (in that webpage, and reprinted here): "I would add one more caveat.. double check that the $SPILL matrix is not just the identity matrix (sometimes this is the case). If so you'll need the single stained controls and the unstained control to calculate the spillover matrix with spillover(), and then proceed as Mike suggests."

Based on the code (without the removed line) the SPILL matrix is the identity matrix `trim_fs`. However, it is still the identity matrix in `fs_comp`, after the spillover command has been run. Did I do something wrong, or is the matrix correctly specified? comp looks like this:

comp

            FL16-A      FL17-A     FL18-A       FL10-A      FL11-A      FL13-A       FL15-A       FL3-A      FL6-A      FL1-A        FL2-A
FL16-A 0.064483949 0.000000000 0.00000000 0.4966442879 0.000000000 1.000000000 0.1093778062 0.515145949 0.00000000 0.00000000 0.0000000000
FL17-A 0.207667955 0.302936275 0.04505139 0.0037973906 0.000000000 0.044282477 0.0009981806 0.004568788 0.11537844 0.00000000 1.0000000000
FL18-A 0.137290369 0.047755735 1.00000000 0.0026519491 0.000000000 0.005856387 0.0009337569 0.002946610 0.62932020 0.00000000 0.0000000000
FL10-A 0.530164933 0.115803952 0.00000000 0.2101694797 0.000000000 1.000000000 0.0491067396 0.289509871 0.00000000 0.00000000 0.0000000000
FL11-A 0.002544856 0.000000000 0.00000000 0.1752085836 1.000000000 0.090981328 0.0273384220 0.033931431 0.00000000 0.04052444 0.0000000000
FL13-A 0.000000000 0.000000000 0.00000000 0.0602779546 0.003245736 0.000000000 1.0000000000 0.000000000 0.00000000 0.00000000 0.0000000000
FL15-A 0.000000000 0.000000000 0.00000000 1.0000000000 0.075268818 0.715053686 0.6912234419 0.342923585 0.00000000 0.00000000 0.0000000000
FL3-A  0.018565235 1.000000000 0.15944549 0.0043590259 0.000000000 0.007846247 0.0020772031 0.004712460 0.05104339 0.00000000 0.0036707592
FL6-A  1.000000000 0.337469559 0.05865700 0.0018091793 0.000000000 0.008401532 0.0006731674 0.002009455 0.02602914 0.00000000 0.0068649689
FL1-A  0.000000000 0.000000000 0.00000000 0.1466463402 0.000000000 0.372256113 0.0367682861 1.000000000 0.24390244 0.00000000 0.1714634354
FL2-A  0.000583422 0.001697758 0.03302168 0.0006885856 0.000000000 0.001562980 0.0001781283 0.011118988 1.00000000 0.00000000 0.0006667258

In addition, the command 

keyword(fs_comp[[11]])$`SPILL`

returns the identity matrix. But should this be the case?

Based on the code available at https://github.com/RGLab/flowCore/blob/23d64cbb635ea7bb131b1047d2b97007b9813d93/R/flowFrame-accessors.R#L437, the compensation matrix is applied but does not seem to be assigned to the header of the FCS files. So what you observed makes sense to me.