Yes, you see the sinewave from your Iphone. But you see it in log mode, as Mark noted. To see real sinewave, you have to change display to linear mode. And you only see it as a sinewave because it it low frequency, so that it passes through your RBW filter and video filter. Change any of both to say 100Hz and you won't see it anymore. But better stop until you have a good signal generator so that it doesn't get expensive.
Secondly you will never ever be able to see broad band signals as with an oscilloscope. Say you set your signal generator to 1GHz. You will see a peak on your spectum analyzer. Now if you set center freq to somewhere inside that peak and set it to 0 span you will see a line, because it is not a modulated signal. With a good oscilloscope, you will see a 1GHz sinewave with 1ns period. Now if you modulate that signal with 1kHz AM sinewave, you'll see a 1kHz sinewave on SA, with 1kHz square wave AM, a square wave. On good oscilloscope you will see 1GHZ sinewave which has gets stronger and weaker @ 1kHz (called signal envelope). That envelope is a square or sinewave. See pics in attachment, how these signals look on real scope (used them when I sold that POS HP-8116 on ebay). Acutally look only on first one, since those signals are all sine modulated square, triangle and sine waves, basically the other way round