I think it’s for the rhyme with “maintenant” two verse above.

Also putting “seulement” at the end is emphasing it.

Moreover there is a comma before “seulement“, so maybe it can be understood as the beginning of the next line: “Seulement, toi, t’y pensais”.

Which can mean: Alone, you were considering it (a breakup).

I also think that here “seulement” is looking like “cependant“, which would mean:
I was just saying but you were really considering it.

According to Larousse, seulement‘s 4th meaning is the French equivalent of however.

Here are examples:

Je t’ai attendu à la gare, seulement tu n’es pas venu…

Moi, je le disais pour te faire réagir, seulement tu y pensais…

Seulement voilà means the same thing but is more insisting.

I’ll try to explain what Stromae meant here:

It’s all about what broken couples might have said. Especially the girls who would say something like "It’s over" only to get more attention from the guys. HOWEVER, the guys can sometimes take it literally.

• "Quoi toi aussi tu veux en finir maintenant ? C’est le monde à l’envers" (Girl speaking to Guy, telling him that she wants to break up and he agrees or at least doesn’t disagree).
• "Moi je le disais juste pour te faire réagir. Seulement, toi t’y pensais" (But she didn’t really mean it but he still did take it as it is)