I have paid 3500$ in taxes last year, yet Turbotax says I will get a 6400$ refund. How is that possible?

Yes, this is possible.  It could be that you are entitled to the working income tax benefit (WITB).  This is a refundable credit intended to provide tax relief for low-income working individuals and families.  If you are eligible for this benefit, TurboTax will automatically calculate this credit based on the info provided on your return.  For more info, please see http://www.cra-arc.gc.ca/bnfts/wtb/menu-eng.html

If you are just looking at the negative figure in the top bar, that amount is what is owing by the time you get to review. 

It is not a negative figure. I entered my T4 info, and on my summary it shows that I paid around 3500$ in tax, further down it says that my tax refund is 6400$, nowhere does it indicate that this is a negative value.

did you have box 118 on your T4?

There are a few other credits that are refundable. The children's activity credit and the refundable medical supplement come to mind too.