Learn Hardcore Swahili: Ukihisi uchovu jioni, pumzika kidogo nyumbani. - If you feel tired in the evening, rest a bit at home.

u- = you (singular subject marker)
-ki- = a marker meaning when / if (ever) / whenever for present or general time
-hisi = the verb root feel / sense / perceive

So ukihisi uchovu jioni is literally when/if you feel tiredness in the evening.

Where is the idea of if / when in this sentence? Why is there no separate word like kama?

The idea of if / when is built into the verb through the marker -ki- in ukihisi.
Swahili often does not need a separate word like kama (if) when it uses the -ki- form.

Ukihisi uchovu jioni = If/When you feel tired in the evening
Kama unahisi uchovu jioni = If you feel tired in the evening

Both patterns are correct, but in your sentence the -ki- form already carries the conditional meaning, so kama is not needed.

Is ukihisi talking about the present, the future, or something general?

Ukihisi with -ki- usually expresses a general or open time frame:

It can mean whenever you feel (a general rule or habit).
In context, it often includes the future: if (at some time) you feel tired…

So it is not strictly “present” or “future”; it describes a condition that can apply any time, similar to English when(ever) you feel tired…

What exactly is uchovu, and why is it ukihisi uchovu and not ukihisi umechoka?

Uchovu is a noun meaning tiredness / fatigue.
In ukihisi uchovu, the structure is literally if you feel tiredness, treating tiredness as a thing you feel.

You could also say:

Ukihisi umechoka jioni, pumzika kidogo nyumbani.
→ If you feel (that you have become) tired in the evening, rest a bit at home.

Both are correct. Using uchovu sounds like feeling fatigue, while umechoka (you have become tired) focuses more on your state rather than the abstract noun.

Could I also say Ukichoka jioni, pumzika kidogo nyumbani? Is there a difference?

Yes, Ukichoka jioni, pumzika kidogo nyumbani is natural and common.
The nuance is slightly different:

Ukihisi uchovu jioni… = If you feel tiredness in the evening… (focus on the sensation of tiredness)
Ukichoka jioni… = If you get tired in the evening… (focus on the event or state of becoming tired)

In everyday conversation, ukichoka is probably more common, but your original sentence is also very good and slightly more “careful” or descriptive.

What time of day does jioni refer to, and why is there no word like in before it?

Jioni means evening, and in practice it often includes late afternoon to early night (roughly from about 4–5 p.m. until it is fully dark).
In Swahili, many time expressions (asubuhi – morning, mchana – daytime, jioni – evening, usiku – night) are used directly as adverbs, without a preposition:

Nitasoma jioni. = I will study in the evening.

So there is no separate word for in before jioni; the single word jioni already means in the evening in this context.

Is pumzika a command here? Why is it not upumzike?

Yes, pumzika is a direct command to one person: rest.
For the regular 2nd person singular imperative, Swahili uses the bare verb stem:

Pumzika! = Rest!
Soma! = Read!

Upumzike is the subjunctive form and can sound slightly softer or more polite, like (that) you rest / please rest, and is also used in longer structures:

Upumzike kidogo nyumbani. = (You should) rest a bit at home.

In your sentence, pumzika is a straightforward, neutral instruction.

What does kidogo do in this sentence, and can I move it to a different position?

Kidogo literally means small / a little, but here it acts adverbially: a little / a bit / for a short time.
In pumzika kidogo nyumbani, it modifies the verb pumzika: rest a little.

You can usually move it around after the verb without changing the meaning much:

Pumzika kidogo nyumbani.
Pumzika nyumbani kidogo.

Both are acceptable. The original order (pumzika kidogo nyumbani) is very natural and perhaps slightly emphasizes the amount of rest before the place.

What is the difference between nyumba and nyumbani, and why is nyumbani used here?

Nyumba is the noun house / home.
When you add the locative ending -ni, you get nyumbani, which means at home / in the house / to home, depending on context.

So:

nyumba = a/the house
nyumbani = at home / at the house

In this sentence, nyumbani means at home.
When speaking directly to someone, nyumbani naturally implies your home unless otherwise specified.

Can I switch the order and say Pumzika kidogo nyumbani ukihisi uchovu jioni?

Yes, that is grammatically fine and understandable:

Ukihisi uchovu jioni, pumzika kidogo nyumbani.
Pumzika kidogo nyumbani ukihisi uchovu jioni.

Both mean essentially the same thing.
Starting with ukihisi uchovu jioni puts more emphasis on the condition first (if/when that happens…), which is the more common and slightly clearer order in such advice sentences.