Hi Minu,
I was traveling yesterday and didn't have a lot of time to look into this. But I did consult with my colleague. One of the reasons behind the discrepancy could be the time signal. Initially we excite all the modes of the geometry, some of these modes (non-resonant modes) would die down, but the modes that sustain will be the resonant modes (modes of interest), and we can calculate their effective indices. It is possible that, in your simulation, the analysis group is choosing a non-resonant mode.
One thing we can do is run the simulation long enough for the non-resonant modes to decay completely. What you can do it turn off the auto shutoff termination (uncheck use early shutoff unchecked in the Advacned Options of FDTD), and run the simulation for a longer amount of time. It is hard to tell by how much longer, I will say increase the time by 20% a couple times and check if you see any differences.
Regards,
Amrita