Is the bank's requirement that an electronic check arrive five days before salaries are disbursed considered usury (riba)? And is there a sin incurred for training employees on this program?

Your work in the company that empowers the government is permissible, and it involves assisting in delivering rights and wages. There appears to be no impediment to continuing in it, as there is no connection between your work and the relationship between the government and the bank. Your work itself is permissible and provides permissible benefits, and the loan process is extraneous to the program.