DO NOT RIDE THIS BIKE UNTIL YOU ADDRESS THIS PROBLEM
Your cables are not properly seated in the levers, and at a hard squeeze (like you'd use if in danger of collision) will burst out the side of the slot leaving you brakeless.
The correct cable has a stepped head
(see Campagnolo or Shimano type) which should pocket completely in the stepped recess in the lever. You'll know it's seated correctly when the wire end of the head is peeking through the fitting a bit.
Slacken the cable, push it free of the fitting (where it's now jammed sideways) and re-seat the head, and you should be fine. If correctly seated, the head cannot escape out the side of the slot.