QRH,
It is a long time since I read the FTL's but having written the FTL's for one operator they kind of stick with one!
What is the heading of the 'split duty' area in the FTL's, does it mention the word 'extending/extension'?
Put it this way, your allowable FDP was 11:30 but, with 3:15 break, it became 13:07, if your operator considered that to be a reduction in the FDP then I suggest that your operator introduce drug testing
I can recall, still, as a young crewing officer, I didn't, then, have the knowledge to live and breath the FTL's, whilst I knew most I didn't know everything and, on occasions, I may have bullsh1tted a crew member making out I knew what I was talking about.
I suspect this is the scenario in your case, in the early days the FTL's are difficult for new/young personnel to grasp, a split duty extends an FDP, it does not reduce it and, even whilst on the split, one remains on an active FDP until the final 'on blocks' of that Duty Period.