I wouldn't say so much it is something in the past, but rather the usage.

With 基, as you pointed out, it refers to based on. Whatever it is referring to isn't something that is being reacted to, though. In order words, the target of the action is not pointed back at the original thing. Using one of the examples from this page:

Model: 「説明書に基づいて自力で本だなを組み立てた。」

Your actions of assembling the bookshelf are not pointed back at the instruction manual - the manual doesn't "receive" the action in any way.

Compare this to に応じて. The most common usage is, as you noted, "in response to"

Model: 「ソフトのよくある質問に応じる内容はこのページにあります。」

In this case, the page includes answers/responses that deal directly with the questions. Put another way, the page is used to satisfy whatever needs the questions created.

Someone else might be able to put up a clearer explanation, but I hope this helps!

The last construction example is poorly highlighted/explained

Examples:

Based on the highlighted area (not the actual Japanese) users might think that it means "History based on tactics." as the explanation states the grammar point is Based on "A" and the highlited word ("A") is tactics in this case.