The Inn reduces resting time after a dungeon - but it doesn't affect every dungeon! The first couple of levels reduce the resting time after the very first dungeon in the game. Then the next couple of levels apply those same reductions to the second dungeon. And so on from there.
So don't worry if it looks like the Inn is saying you're still currently at 100% resting time - it's showing you the reduction for the next dungeon down the line! All the previous ones are already benefiting.