Generally, you should not have idle workers and tile improvement should be paced to stay well ahead of population growth. First, you don't want citizens working unimproved tiles, if at all possible. Second, you will likely need/want to switch citizens between food, hammer, gold, faith and culture tiles, which you can't do (without violating principle 1) if those tiles are not already improved. It's important to note that, except for roads and railroads, tile improvements do not have a maintenance cost, so there is no "penalty" for improving tiles before they are needed (other than opportunity cost associated with improving these tiles vs. those tiles).