need to take a week off internship for exams

You should tell them the truth (don't claim it's some family emergency, or similar).

However, you can control the timing of that truth. If you think there's a genuine risk that they'd revoke the internship, then it might be wise to delay telling them. You should give them at least two weeks' notice though - more if you can. And you should be honest about the reason.

It's not like you've failed any exams, right? You just deferred taking them for health reasons. That's perfectly reasonable, and eminently sensible.

would like to tell them the truth too, but if i tell them before the internship starts, there’s a high chance they may revoke my offer since i am not able to meet their terms and conditions for the duration requirements. and if i tell them after my internship begins, even if early, it will make me look irresponsible for not telling them earlier when i already knew i’d have to sit for my exams during the deferral period when i had to defer it. so i am still unsure about this

i guess i’ll have to go with the latter.i think i’ll tell them after the first week of my internship that i deferred my exams bc of health and only recently found out the deferral period will be taking place in august. i’ll also offer to extend the internship period after i come back to make up for all the days i was gone. hopefully it’ll go fine and they won’t revoke my internship!