I think, perhaps, that poison isn't the right term here.

There are certain drugs that result in bloodshot eyes - and more to the point, violent hallucinations. That Beat would attack May in the chapel with the sole intent to murder her is both not terribly in character and quite stupid. He could only have known that May would be in the chapel if he overheard her discussing it with Kaoru, at which point it would be obvious the two of them intended to meet in the chapel. He wouldn't have planned a murder where Kaoru could have walked in at any moment. It was entirely unplanned that she was delayed.