This might sound crazy but I think the key to getting those weird Idolm@ster symbols (which apparently increase the chance of getting presents) is tied to getting perfect timing with your notes.
I'm able to consistently get these symbols from my notes (at least every two or three notes, and usually an entire stream) by adjusting my timing a little bit with my notes.
Since I've started adjusting my timing I've been able to consistently get a present each time (actually just got the S rank DL costume from doing this).
Maybe I'm just getting super lucky, but it's worth looking into

Edit: Nevermind I don't think this is it. I got these results for five songs in a row but after I tried the last DL event with the S rank costume I couldn't get it to work. Maybe it is just random.