Half of that tax is paid by the employer and is not coming out of the salary, but it is in addition to it as an expense. The benefit directly to the pay check is only half of that check.
You're right, there is no guarantee that the amount paid by the employer would end up in the employee's paycheck. However, it is all essentially payroll expense to the employer, regardless of if it's paid to the employee or the government. Paying it all to the employee would leave the payroll expense as is. If the company kept that portion, it would be an additional savings, on top of the corporate income tax reduction, and would end up in price reduction of their product. So, either way, the savings would end up boosting the economy, either by increased income for the employees or decreased prices for the consumer.