I was trying to power my servo and the idea of powering it through a powerbank by using the usb breakout seemed to be pretty decent to me. But seconds after connecting my motor to it , the servo started getting hot and is not working now.
I was wondering why that happened as the output of the powerbank is 5v and I checked it too with a multimeter. I thought the current required will be drawn according to the motor need.(is this assumption of mine wrong?) or is there something else that I missed.
A 5V powerbank yes. I have no idea what "a breakout board" means to you but most of the ones I know of don't power anything, they need power themselves.
There is another path to the overheat failure you experienced.
If you can power a servo with a proper power source and then command the servo to move, but prevent the servo from moving, it will overheat and fail.
Some servos have a range of movement limit and if you drive them beyond that limit, they bind and overheat.
Or maybe you have something attached to the output arm of the servo that was preventing the servo from moving.