There was massive chaos on that plaza. Hundreds, maybe even thousands of fishmen were running around and screaming as a result of the fire. That was probably also the main point of setting it on fire. Not just to get rid of the signatures, but also to create and opportunity where Otohim would have difficulty to sense the incoming attack. Coby already showed that he was going nuts of hearing the voices of all those marines dying. Otohime was more adapted to Haki than Coby, however even she must have had difficulty to have her Haki work properly amidst all that chaos. For someone who uses the CoO, that's the worst case scenario. Considering the importance of those signatures to her, she also might have been emotionally less stable than normally.
I don't really see any kind of plothole here. I've read something similar once in another manga where there was also a person who had the ability to sense people. They tried to kill him by intentionally staging a large scale battle so that they could use the turmoil caused by all those soldiers to stab him in the back.