"The next tax year, I will include the employers payroll tax portion as a deduction for which they will get the write off in that year."

That isn't how Payroll in the US is treated. You are confusing Banking and P&L.

"So you're saying the bonus can't be written off in 2018 because it didn't hit the employees account?"

That's right. Payroll is a cash-basis event. If you don't pay it, it isn't expense. And the employer liability is triggered because you paid payroll, which makes the Pay Date the date as expense for everything we are discussing.

Gross Wages + Employer taxes = total expense for that pay date

The banking is:

Takehome pay + Liability (to be paid later) for that same date 

The Tax Due Date might be 3 business dates, monthly, or even the 940 might be once a year.

There are a few things different for accrual entities, such as governmental units.