While Jelena may be (or were) trading songs about each other on their records by no means were they the first. Quintessential 90s kids will remember when the IT couple were Justin Timberlake (JT) and Britney Spears. The most obvious trade is that of JT referring to Spears' "I'm A Slave 4 U":
(Video released 10/24/09) in his "SexyBack": (Video released 10/02/09).
Also famously, after their infamous 2002 split (the videos may have been released almost a decade later, but clearly they had each other in their minds when writing and singing them) JT made a very widely rumored video about their breakup, "Cry Me A River" (also uploaded October 2009): which is the more famous allusion song. However Brit Brit also had her own JT break up song in "Everytime" (also a 2009 upload):