In case of e6 there are, basically, two alternatives:
- Nf6, transpoing with e5 Nd5 ... d6 and so on or playing something else without d6
- d5, playing in a french style.

Regarding the later, If you play e6 with the french idea in mind,there is always this annoying isolated pawn possibility

1. e4 c5 2. c3 e6 3. d4 d5 4. exd5 exd5 5. Nf3 (and now a6 or Nc6 normally). 

You have to be willing to play this structure, which is very easy to play for white. So, not a good try for a win.

There are alternatives. Instead d5, playing with b5-d6-Nf6 .... But, again, white has a good control of the center and a more confortable position.

Appart from this you have the chance of ending in a french advance, which you need to prepare. Lines with a3 or the milner-barry gambit need its previous work. Others are more intuitive ... but not easy at all. 

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The Chase Variation can be a useful practical choice. The point being that if you face the Alekhine very infrequently, transposing to something you get more often has its subjective points. It's all relative, but from a 2000ish perspective, the lower rated player will not handle Alapin positions well. 

That makes it a good choice for 2000 v 1700 but a bad choice for 2000 v 2300.

I'm no Alapin expert, but it makes sense for Black to keep as many good setups as possible on the table for as long as he can, to keep White guessing. 

With that in mind, 5...d6 makes more sense than 5...e6. The only setup Black "loses" by playing 5...d6 is the one with an early ...e6 and ...b6, and most books consider that dubious anyway (though don't ask me if that conclusion still holds up).

One big reason Black players still regularly reach the position after 5...e6 is ...e6 was actually played earlier - via the move order 2.Nf3 e6 3.c3 - which as I've just argued limits Black's options. The ones he has left are still supposed to be good enough objectively, of course.

MNb wrote on 11/17/19 at 12:42:25:

Doesn't Black usually develop the c8 bishop before playing ...e6 in the Alekhine?

I have trouble with this too, so my advice won't be much use to you. What I can say is that the positions with ...e6 seem quite scary to me, and this impression is not dispelled by examination of Kotronias' recommended lines. Indeed I would play c3 myself if everyone played this way as Black. Kotronias points out that it is playable after 2.Nf3 e6 3.c3; but, for me, 3.c3 is a good reason not to play 2...e6. I'd rather face the Rossolimo.