As said, you need one IF your home's water system is closed. A closed system means water can come in but is blocked from going back out. This can be caused by a check valve or a PRV (pressure reduction valve, even if it has a bypass). If you do not have a closed system, you do not need one unless your local codes require it (some do). The reason is that when the dense, cold water goes into the tank, then gets heated, it expands. Since few of the pipes are elastic (say the washing machine hoses, and some supply lines to the toilet or faucets), but most of it is pretty solid, the pressure rises almost instantly. Some stuff can swell, and some may leak, which relieves that increased volume and therefore the pressure. The definitive way to tell if you need one is to buy a $10 water pressure gauge, put it on say a hose bib or the drain of the WH, and leave it there for 24-hours. If you get one with a tattle-tale (peak reading hand), and it rises above your normal pressure, then yes, you need one. If it doesn't rise, you probably don't unless codes require it. Note, many water utilities are going around and putting new meters and check valves in. This could change your system from open to closed and you may not know about it. If you had a functioning expansion tank, you'd never know. If you don't, you'll probably get discharge from the safety T&P valve on the WH. Depending on where that is, you could get water and mess up the floor or walls. It isn't much, but it happens after any significant hot water useage.
Technically, code requires items to be installed per the manufacturer's instructions. SO, even if you wouldn't normally need one, if an inspector read the installation instructions, he would require one to be installed, because the manufacturer requires it (if I understand what you said from the instructions). Now, they rarely read the installation instructions....