"Some players use chinrests that sit over the tailpiece but also extend over to the left."
This chin rest allows you some flexibilty in whether your head contacts the instrument mainly with the jaw or more towards the chin.
The placement of the violin needs to suit the length of arm of the player. If the violin is too far to your left unless you have long arms you will not be able to reach the point of the bow (particularly on the D and G strings).
To help place the instrument it is good to practise without a shoulder rest so there is more flexibility in where the violin sits on the collar bone.
The Violin & Your Body - Holding the Violin