F-1 to H-1B, need to pay FICA for when I was still in F-1?

I just recently changed my status from F-1 to H-1B, and now I owe all the FICA taxes that I was supposed to pay for when I was still employed on an F-1 visa with OPT.

 

I know that as an F-1 student we're exempt from paying FICA taxes, and my most recent F-1 visa in my passport was from 06/2017. However, once I switched my status from F-1 to H-1B and let my employer know about the change, they told me that I'm now liable to pay for the FICA taxes for when I was still employed as an F-1.

 

Is this correct, or is there some kind of misunderstanding? Do I have to back-pay my FICA taxes for when I was still employed as an F-1?

 

Timeline (I pass presence test for all the years):

08/2011 - 12/2015: F-1 visa, undergrad student

01/2016 - 09/2016: F-1 visa, further education student

09/2016 - 03/2018: F-1 visa, grad student

03/2018 - 10/2020: F-1 visa + OPT, employed

10/2020 - Present:   H-1B visa, still employed