Learn English – “good about 〜ing” versus “good at 〜ing”

"I'm good about" is a colloquial expression, similar to "good at," but expressing a tendency to be disciplined about certain things, and can be trusted to do them:

I'm good about not eating after 8pm.

I'm usually good about not putting my ex-husband down in front of the children, but sometimes I just lose my cool - especially on the phone.

My sons are pretty good about cleaning up after themselves. I hardly ever have to remind them.

"I'm good at" expresses a talent or affinity for something:

I'm good at editing and I'm a fast typer.

My wife was very good at bookkeeping - she paid all the bills.

In your sentences, the first one expresses that the speaker knows that things have to get done and is disciplined about doing that, does them in a timely manner. In the second sentence, the speaker is very talented in that respect and knows how to get things done, it a good time manager, etc.