Laurel is broadly right, but there is a peculiarity in your first example that I can see would make it confusing. It’s that em-dash between “bad” and “tempered”, giving bad—tempered. Because it’s a dash, it leaves the two words separate. The “bad” means “bad news”, in reference to the earlier mention of good news. And so the “tempered” stands on its own and is a verb, meaning to balance, or moderate, or dilute, etc. But if the reader mistakes the dash for a hyphen, then we get the adjective, “bad-tempered”, meaning grumpy, or annoyed, or mildly angry (and which breaks the sentence and makes no sense).
Given all that, the intended meaning here, of “tempered with” is “balanced with”, or “moderated with”, and so on. In other words, the speaker is saying that they are going to do something to compensate for some possible imbalance created by something else.