PLUS loans do not act like other federally backed loans in many instances. For example you have to apply for them based on credit (whereas a denial for a federal loan is almost unheard of unless you go over the aggregate amount).
Another big difference is in the grace period. PLUS loans do not have a grace period. They will enter repayment as soon as the loan is fully disbursed and after the borrower is no longer enrolled as at least a half time student.
But there is a solution. You can apply for a Post-Enrollment Deferment. This acts like a grace period and lasts for six months after the borrower or student the loan was taken out for graduates, withdraws, or stops attending at least half time.
For a Graduate Student this should be requested near repayment, typically 60 days. For a Parent PLUS loan when you are requesting your Parent PLUS In-School Deferment you can request your Post Enrollment at the same time.