Der Wissenschaftler erläuterte genau, wie er bei dem Experiment vorgegangen ist.
Should not ist in this sentence be sei (the Konjunktiv I)?
The basic question is: in the indirect speech, when to use Konjunktiv I and when not?
The subclause in question is not indirect speech; it’s a relative clause or modal clause (depending on your choice of categories). You can test this easily by trying to express this with direct speech, i.e., with quotation marks – which is impossible here. This works in both, German and English. For example, the following does not make sense, because the scientist did not say what is put in quotation marks:
* Der Wissenschaftler erläuterte: “Wie ich bei dem Experiment vorgegangen bin.”
* The scientist explained: “How I performed this experiment.”
As this is not indirect speech you cannot use sei (Konjunktiv I) here no matter what you want to express.
A similar sentence that would contain indirect speech would be:
Ich fragte den Wissenschaftler, wie er bei dem Experiment vorgegangen sei.
I asked the scientist how he performed the experiment.
Here wie is an interrogative pronoun (of the indirect speech), not a relative adverb. Therefore in old grammar or very formal grammar, we have to use sei (Konjunktiv I) because it’s indirect speech. Nowadays, this is not consistently used anymore though, and I thus wouldn’t consider using ist (Indikativ) wrong.
Note that the above test now works and we can replace the indirect speech by direct speech:
Ich fragte den Wissenschaftler: »Wie bist du bei dem Experiment vorgegangen?«
I asked the scientist: “How did you perform the experiment?”
Sidenote: Using wäre (Konjunktiv II) is possible in both cases. It signifies that the scientist did not perform the experiment. There is some implicit, irreal condition (that should be clear from the surrounding context). For example, the scientist is talking/asked about an experiment that somebody else performed and he would have performed differently:
Der Wissenschaftler erläuterte, wie er bei dem Experiment vorgegangen wäre [wenn er es durchgeführt hätte].
The scientist explained how he would have performed the experiment [if he had done it].
Ich fragte den Wissenschaftler, wie er bei dem Experiment vorgegangen wäre [wenn er es durchgeführt hätte].
I asked the scientist how he would have performed the experiment [if he had done it].
Der Wissenschaftler erläuterte genau, wie er bei dem Experiment vorgegangen ist/sei/wäre.
All variants are correct, but they mean a different thing.
If you use ist, the scientist tells what he himself did. Not about what he heard of. It's a fact. No place for the Konjunktiv.
If you use sei, people will automatically assume er is a different person than the scientist. Because then, it's hearsay. May be true. May be not. The Konjunktiv I conveys that.
If you use wäre, the scientist tells the experiment he would have set up would be different from one he described before. But his experiment did not happen. It's a counterfact. That's what Konjunktiv II tells.
In short: Konjunktiv I is about uncertain facts. Konjunktiv II is about counterfacts. That's why they are used for indirect speech, thoughts and conditionals.