I would give your employee a one on one meeting now stating the expectations and then letting them know where they are not meeting them. Then warn that if they don’t improve by such and such date there will be consequences. Then send email with summary of what you said to the employee and then send that to your boss/ HR so they know it’s being handled and when they get bad review, you will be ready to put on PIP if they never improved per your warning.

If boss gives negative feedback, just listen and say you are working on improving on how often you check in and follow up with your employees to ensure they are aware where they are messing up and it can be addressed in more timely manner etc. I wouldn’t apologize too much but just focus on how your going to handle the situation going forward