Goodness me, have the parents told you that all screen time is banned? Difficult if you have gone against their wishes, but I can totally see the attraction of 20 minutes peace when he has been so good all day. Looking after a toddler 3 days a week is an incredible imposition, and perhaps you need to suggest other ways that you could get a rest, and reward him for being such a good boy. Blaming you for any temper tantrums is totally unfair.
Hopefully this will blow over quickly and if you do need to resort to screen time as a last resort in the future, keep quiet about it!
(Yes, I know, parents rules to be respected at all times, but surely we should have some sympathy for the OP, I know I have!)