Officials said all bands should play a single drumbeat while passing St Patrick's RC Church on Donegal Street.
However, the Glasgow Orange Defenders Flute Band, from Yoker, is thought to have broken the order.
Stuart Leckenby, band sergeant, said on Facebook: "If asked if I would change or play anything different? Never. We are what we are."
A spokesman for the Police Service of Northern Ireland said a review of footage is being undertaken.