ac/dc adapter input amperage rating
Your post is incoherent since it is super not obvious what connections there are or if you are even talking about two, three or four components. You refer to control circuits and devices which may or may not be the same thing; I can't tell. Things with plugs seem to be plugging into outlets that may or may not be located on the wall or transformer; It is unclear.

Picking the only part that made sense:


  device's ac/dc power adapter has an input rating of up to 1.5A on from 100-240V then won't potentially blow your secondary fuse on the transformer since it is pulling 1.5As? 


I'm assuming this is the answer to your question.

The input rating on a power supply is what it pulls when providing the maximum output rating. In the same way the maximum output of a power supply doesn't mean it must to supply that, the input rating doesn't mean it must to pull that.