Relay is a load device so you do not need that fuse inline but you will need a powerkit installed in parallel to the relay coil. I would take the fuse out. You will need to make sure that the relay is an AC type relay not a DC if your transformer output AC. I am not sure what transformer you have in the picture but it doesn't look like our average standard USA doorbell transformer which is an AC.
if the relay is activated (contact closed) then
@Jack007 may be right that you have the relay connected in parallel with the transformer powering it all the time. it need to be in serial to the doorbell button and transformer. jack also mentioned to check the diagram on page 101, just replace the chime with relay in that diagram then you should be good to go.