Spec are a funny thing. Relay are funny too. They have an in rush of current and then settle to a lower value.
If it was me I would want a controller to handle at lest twice the current of the input control of a relay, So I would say you are good to 2.5 amps. I just did a quick search and found a 150 amp relay with a 1 amp input current hold but start up resistance was 0.2 ohms. ( it would try to draw about 60 amp for a very very very short time.) So not sure what your question is.