I'm not a big fan of this particular definition as contracts can come into existence in many ways.
You will need to apply the law on contract formation to establish when a particular contract came into existence. It could be when the parties sign the contract or it could be when one party makes an offer which is accepted by the other (such acceptance could be by conduct).
In your example, it would be when the Employer has accepted the Contractor's offer, but more would likely be needed than just sending the contract to be signed as that may be seen as a counter offer.
Each will turn on the particular facts.