Stupid question, but...Hardback measurements and templates

For those of you who have published hardbacks, I have a question. I’m getting ready to publish one and realized the inside pages are trimmed smaller than the cover. Duh. But does this mean that the measurements I choose (say 6×9) are the exact outside measurements? And then the publisher will trim/scale down the 6×9 formatted pdf template I’ll give them of the interior. Or does the interior require special formatting in some way?