Rebbetzin, Rebbi came home for kiddush, not havdala. That he was motzi his family, and therefore had to have a din of a living person at those moments, is in Sefer Chassidim. But the rest of the time he had a din of a meis.
In general, the definition of “dead” when we talk of tzadikim is vague. It’s clear that tzadikim are capable of things in “death” that most people are not. Not only Rebbi coming home to make kiddush, and all chachomim moving their lips when their torah is repeated, but also R Elozor br Shimon lying dead in his attic for years, answering shaylos!
(Though even normal people are capable of things that goyim and apikorsim deny. Yidden believe that the dead are aware of what happens to their bodies and at their graves, and that if you visit their graves and speak to them they listen.)
But they are still “meisim” because that is what the Torah calls them. Avrohom and Yitzchok are meisim. Moshe is a meis. R Elozor br Shimon is a meis, and was one even when he was in the attic. The only two people whose demise is recorded in Tanach without the word “meis” being used are Yaacov and Dovid. The gemoro discusses what exactly this means, and the conclusion is not clear, but Rashi understands it literally, that Yaacov and Dovid are lying in their graves, alive in the normal sense, even though they have nothing to eat, etc.
(On the other hand there are contexts in which the Torah uses “meisim” to mean resho’im, even when they’re physically alive, and “chayim” to mean tzadikim even when they’re physically dead.)
Also see the Shaloh on “Yaacov lo meis”, who explains that Yisroel died but Yaacov didn’t, because he had already died years earlier and had come back to life, so without Yisroel he was like people will be after techiyas hameisim.