Wires not snapping to pins on component in Altium 19
So turns out, the problem did lie within the Schematic Symbol designing. I didn't realise when you attach pins, they have a 'direction'. 

I was placing the snap point of the pin towards the inside of the component rather than the outside during symbol designing, so this meant unless I was placing wire directly to the far end of my pin in the actual schematic, nothing was actually connecting.

Flipping these pins and updating my schematic from libraries fixed the problem completely! Hope this helps someone, someday.

I've attached an image that shows when the pin is now the correct direction, the tiny little white dot on the end symbolises the snap point.