You can say ‘I’ve got them covered.’ It doesn’t mean, however, that they are generally taken care of. ‘Covering’ often has to do with paying something or doing some specific task, perhaps administrative. A: Who’s going to pay for the visitors’ lunch? B: I’ve got them covered. (Or ‘I’ll cover them.’) A: Their applications have to be submitted by Friday, and they haven’t started. B: Don’t worry. I know. I’ve got them covered.

Hi Dimin, I hope that you are well. "You got covered", will not work in this context. " I have these people covered" is better suited I hope that helps.

It doesn't really sound natural to be honest. It is better to say these people will be taken care off.

Get not got, or maybe are. Personally I would say 'I will make sure these people are taken care of' or '...are looked after'.