After researching this some more and working with test data, I found this message in the 2021 version regarding which transformation that was selected. So it was just that the transformation that was used had changed between the versions.
2021.1 FME
CS-MAP Reprojector: Transformation will be automatically selected for 'LL83_2011' -> 'TX83-CF', and is not guaranteed to remain the same in future releases of FME
Reprojector: Using transformation `NAD83_to_WGS84,Forward(Null,EPSG:1188)' when reprojecting from LL83_2011 to TX83-CF
Reprojector: Using transformation `NAD83_to_WGS84,Inverse(Null,EPSG:1188)' when reprojecting from LL83_2011 to TX83-CF
I then looked at the 2022.1 version and read this message in the log file.
2022.1 FME
CS-MAP Reprojector: Transformation will be automatically selected for 'LL83_2011' -> 'TX83-CF', and is not guaranteed to remain the same in future releases of FME
Reprojector: Using transformation `WGS_1984_ITRF08_TO_NAD_1983_2011,Inverse(Bursa Frame Rotation)' when reprojecting from LL83_2011 to TX83-CF
Reprojector: Using transformation `NAD83_to_WGS84,Inverse(Null,EPSG:1188)' when reprojecting from LL83_2011 to TX83-CF
If you have used TX83-CF as coordinate system in previous version and notice in data shift, try use NSRS11.TX-CF instead. This will put it in the correct spot. Looks like transformation that apply to the non-2011 coordinate system version has been change and we not sure how apply change to transformation currently.