What do we do after missing the 2nd rukuh in Friday Congregational prayers (Jum'ah)

So I live in KSA, and I arrived late at the mosque and I joined the jamat at the second sujood of the second rakat, so after I finished two rakat the one next to me started his 3rd rakat I became confused and out of fear (that my salah becomes void) started my 3rd rakat and then 4th (as stated if you miss the two rakats of jum'ah you must pray 4 rakats). So can you please help me, I'm a little confused?????