Since Mr. Jackson became president, unemployment has increased.
I know a time clause might refer to a particular point in the past. But the question is, Is Mr. Jackson still President?
She hasn't been able to play tennis since she broke her arm.
Is her arm still broken?
When we use the present perfect, we are choosing to present the events described as having some particular relevance to the present. (Often we could also choose to present the same events without that, by using a different verbal construction).
Exactly what that relevance is, is not defined. Sometimes it is that the events are very recent. Sometimes the events refer to a state which is still continuing. Sometimes the speaker is choosing to refer to a period stretching from the events to the present. And there are other possibilities.
Only context and real-world knowledge can distinguish between these - and in the absence of context they may remain ambiguous.
Your questions are both about whether the second interpretation above ("the events refer to a state which is still continuing") is the right one.
And without context, the answer is always "it might be and it might not: we cannot tell".
In the first case - it is hard to imagine a situation in which the knowledge of "who is president" is not generally known. This looks like a political debate so you can be sure that everybody involved knows who is President.
Grammatically it doesn't imply that Jackson is President. You could say, correctly, "The USA has become larger since Washington became President". But in the context of the debate, presumably Jackson is still President, since that is the political point being made.
In the second, Her arm could have healed. She might not be able to play tennis because of a phobia of breaking her arm again, or because she broke her racket in the same accident that broke her arm or for other reasons.
Again you probably don't need to grammar to tell you if her arm is broken or not. You probably already know.
