Note: None of this should be taken as tax or legal advice

No.  Defined contribution health plans do not need to be funded until an actual reimbursement is made.  A company is not required to fund any portion of employees' defined contributions in separate bank accounts.   

In fact, it is recommended that the company keep the defined contributions in their own bank accounts (e.g. a general purpose bank account) and handle reimbursements via payroll for maximum savings and control.