Learn English – Which tense should be used after word after

Among the three samples you have provided, the middle one is correct:

I will update you once I reach my home.

The first one is wrong because you are mentioning there that you'll do something in the future after you do something in past(which of course doesn't make sense).

Same situation arises in the third one.

Again, as @StoneyB mentions:

get is a much better choice here.

In sentence 1, both verbs, make and wake, are in the present tense, but in English the tense (i.e., the verb form) doesn't always refer to the obvious part of the timeline. Here you might reasonably expect the current time, but this usage talks about a rule that's true in general. You should have made your bed when you were a kid, you should be making it now, and you should make it for the foreseeable future. (At all times, after you're awake, of course.) This is sometimes called the enduring present tense.

In sentence 2, the normative aspect (the "ought to", the should) still expresses the general rule, but woke (the past tense of wake) conflicts with that rule since woke is confined to past action. This makes the sentence ungrammatical. If you want to keep the waking in the past, then you have to transpose the bedmaking to the past as well:

2a. You should have made your bed after you woke up.

Of course, that's not a general admonition; it's about just that time after you woke up.

So why does 3 work, with the waking in the present perfect (have woken)? The clue is in the name. The "perfect" means that the verb speaks about completed action, and the "present" means that the action takes places at any time up to the present or that it affects the present. That necessary reference to the present is missing in the simple past in sentence 2.