is the melting curve showing higher or lower Tm? it may be that in absence of template (in the control or treated samples) primers form dimers and you are seeing those? 

How does the negative control (without template) behave?

try to run your samples and negative control on agarose gel, to check the size of your amplicons in treated and control samples. A remote possibility (but still a possibility to be checked) is that your primers detect a splicing isoform induced by the treatment. 

When making the reaction perhaps you accidently put two different primers in the sample reaction, one for gene of interest and other for target hence two different curves?

Hello Johnson

I would say that if you don't expect a second specific product what you have is a second non specific product in the same abundance as your specific band

What are the melting temp. of your primers ? Just like gel based PCR you should tailor the annealing temp of your reaction in qPCR and not simply always follow the standard reaction conditions as many people do

When I perform qPCR I tend at first to screen my primers by gel based PCR and if necessary run an annealing gradient for new primers: This gradient tends to run from Tm+1C to Tm-5C in 0.5C to 1C intervals. I then pick the Ta that only yields one specific product in the largest amount and use that as my Tm in qPCR. Generally speaking Tm-2C for both qPCR and gel based PCR works best

So you could either verify your primers on a gel: In your case I would simply increase the annealing temp in 1C intervals until you just have one specific band or simply try increasing the annealing temp in your actual qPCR in 1C intervals if you wanted to dispense with agarose gel based screening