Sorry to say, but this does sound like a typical lease. I am not suprised that they are evicting you this early. If you think about it from their standpoint, if you missed rent on the first month (or incomplete rent) then that sets up a pattern saying you will probably be unreliable. So if they evict you know which they can if the rent is not paid on time, and in full then there will be minimal wear and tear to the apartment since you have not been there for long and they can get someone who is unreliable out.
I would definatly talk to them, tell them your situation and see if you can work something out! Maybe they can let you stay and maybe they can at least give you your deposit back so you can find another place. It's just one of those live and learn situations. Always pay on time and in full or they can seek eviction even if you are only 1 day late!

