Apply today start tomorow is a lie right?

Logically one would consider this kind of promise to be misleading. After all even if you do apply today, it's doubtful they'll have time to process all the applications, choose someone, contact them and then have that person start the very next day.
I believe what they mean is they need someone immediately, so they only want people to apply who can start the moment they get the job, rather than someone who has to give their previous job notice or who just isn't available to work for a few weeks or months.
If you're seriously interested in the job in question I'd contact them, and ask when they 'tomorrow' how soon do they really mean. That would clear up any confusion.