Is it normal for rabbits to always act like they're hungry when presented with a new batch of hay/pellets/greens?

If you like to understand the behavior of your rabbits at home, you could try a look at the rabbits in nature. (The domestication of rabbits is not long enough to destroy all their behaviors they learned/stored in million years of free life.)

Rabbits in nature have every time (without little times in winter) a lots of food around them. They live in a green environment with grass, leaves and dry grass (hay...) everywhere. If they could choose they favorite fresh greens against hay. Even in winter they dig into the snow to find "freeze-dried" leaves and greens from autumn. And the wild ones do not get fat :)

Rabbits are semi-active. This means, they are awake for 2-4 hours and then sleep/rest/doze for around 2 hours. For example my two are active in the morning, then make a early nap, are active before midday, make a nap when it is hot, are active in the afternoon and make a late nap before they are active in the dawn again. The night has a alike structure. This lifestyle and their digestive system are cause for their eating-behavior: they hop a little, then eat here a leave, hop, eat, hop, eat... and so on. The food transport inside of their body is not made by muscles (like in humans) but by "eat again and push the previous meals down the pipe". (They have muscles too, but the main movement is caused by eating).

Next point: in nature rabbits drink only in few occasions. They eat a lots of fresh greens and that gives all the water they need. In winter they sometimes eat snow, because the food is dry. Same for grains (and pellets that base on grains): they get them only in the autumn, when grains grow on the grasses. Then they are very affected by them, because they like to get enough fat before the winters come.

And last: Rabbits do not eat hay, they used to lay on or even peed on. This is a hygiene mechanism to save their health.

What could this mean for you:

• low energy food available every time (hay, but better fresh leaves if available for you)
• hay into a hay rack (inform about the differences between risky and save constructs)
• high energy food (pellets, grains) should be measured
• if you could achieve it, split the feeding into more than two meals (or place the meals in a way, the rabbits need to do something for their food, then they may spare some for the next active period)

Long to short: For the "traditional" way to feed rabbits (like it is done for years and years), Yes it is normal for your rabbits to act like starving. They had active periods without food, which is not normal from their point of view.

(If you have the chance to get fresh greens from a meadow/green yard/garden/balcony or somewhere alike, and the patience to look on a lots of photos to find plants that you know, then I could recommend you this website: List of wild herbs on kaninchenwiese.de. It is in German language, but all wild herbs are with image and botanical name. If you use some translator, like for example google, you could understand the additional information about every plant too. For example if they could be fed without limit, or if they are helpful for some health issues. So you could bring your friend a little present from every walk you do outside.)