Huge River Paradox

[Ceru]

Hi, I'm currently making my map for a fantasy series following this tutorial. However, after observing it a little more, I realized there is river paradox going on here. As you can see in the attachment, the dark black lines are where the rivers are supposed to be while the white lines will be the real rivers in the final mapping stage. The biggest white line going down nearly in the middle is where half of the problem is.

Several dark lines flow from both sides of the mountain and instead of coming together to form a valley or something, they flow north, creating a huge river up there and ending at the west coast. I know and read that all rivers flow downhill hill, but for this map in particular, the smaller rivers are flowing north instead of south, which makes no sense (since gravity pulls everything down, I'm assuming most rivers would flow south because 'south' is 'down') so, I just can't imagain it going up north.

I am considering whether or not I should just disregard the render (thus why I have a huge white line there, more of which I will add later so that it will hit the sea). However, I then realized why the render came out that way: because down south, there were also mountains so then it kind of made sense why the rivers would be flowing north instead of south... water has to flow somewhere and since there are mountains west, south and east, the only exit left is north... but, how realistic is this? Is it possible for rivers to flow north if there are hills on all sides? Is there anyone out there who knows a fair amount about rivers who can give their thoughts on this?