If I received a T4 late, do I simply need to fill out a T1 adjustment in order to include it on already submitted taxes? What about provincial?

You will need to wait for your Notice of Assessment since CRA may have had a copy before you did of your T4 and if so, they would have fixed your return. 

Once you receive your NOA you will be able to verify if it was added. If not, then yes, you will file an adjustment on your T1 only.  CRA will assess your return and if anything changes they will advise you.