The passuk in Devarim (31:19) reads: ועתה כתבו לכם את השירה הזאת ולמדה את בני ישראל שימה בפיהם, "And now, write for yourselves this song (i.e. the Torah) and teach it to the Bnei Yisrael; place it in their mouths." The Gemara (Eruvin 54b), אל תקרי שימה אלא סימנה, "Do not read it as 'place' but rather 'mnemonics.'" (Translation to both is mine, based on Rashi ad. loc.)
The sugya is clearly talking about ways to remember Torah learning more easily, yet I have often heard (and seen on this Tikkun) this derashah misapplied as a hint to leining with trop. Is this a common misconception, and if so, where did it start? Is there another source that explicitly applies the same derashah to leining instead of mnemonics?