I would have thought you'll have a standard pot sitting on top of the chimney brickwork and then flaunched around. It's fairly common for the joint between the pot and the flaunching to crack and allow water in, which then runs down the liner and settles on top of the register plate. If you can get at it a good quality polysulphide sealant will sort it out. (polysulphide because it's semi setting and won't dry out and crack in the sun)