Dayım salataya havuç ve mayonez eklemiş olmalı, tadı biraz farklı olmuş.

Dayım means my maternal uncle.

It breaks down like this:

• dayı = maternal uncle
• -m / -ım = my

So:

• dayı = uncle (mother’s brother)
• dayım = my uncle

This is a very common pattern in Turkish kinship words:

• annem = my mother
• babam = my father
• teyzem = my aunt
• dayım = my maternal uncle

A useful cultural/language note: Turkish distinguishes different kinds of uncle more specifically than English does.

• dayı = mother’s brother
• amca = father’s brother

Because eklemek usually takes something to which an item is added, and that noun goes in the dative case.

• salata = salad
• salataya = to the salad

The ending here is:

• -a / -e = dative
• because salata ends in a vowel, Turkish inserts a buffer consonant:
  • salata + ya → salataya

So:

• salataya havuç eklemek = to add carrots to the salad

This is very natural Turkish with verbs like eklemek.

Because they are being used as indefinite direct objects.

In Turkish, a direct object often appears in two ways:

• bare form for an indefinite/non-specific object
• accusative form for a specific/definite object

Here:

• havuç ve mayonez eklemiş = he must have added carrot and mayonnaise
  • not a specific known carrot or a particular mayonnaise, just those ingredients in general

If the objects were specific, you might see:

• havucu ve mayonezi eklemiş

But in ingredient-style contexts, the bare form is very common and natural.

eklemiş olmalı means something like:

• must have added
• he probably added
• I conclude that he added

It combines two parts:

• eklemiş = apparently/it seems he added / he added (inferred, not directly witnessed)
• olmalı = must be / must have / probably

Together, they express deduction based on evidence.

So the speaker is not saying:

• I saw him add it

Instead, the speaker is saying something like:

• Given the taste, I’m concluding that he must have added carrot and mayonnaise.

The suffix -miş / -mış / -muş / -müş often marks:

• information not directly witnessed
• inference
• hearsay
• realization after the fact

Here it is especially about inference.

The speaker tastes the salad and concludes something. So eklemiş fits well because the speaker did not necessarily watch the uncle add the ingredients.

Compare the feeling:

• ekledi = he added it
  
  • more direct, more neutral, more like a simple fact
• eklemiş = apparently he added it / it seems he added it
  
  • based on inference or indirect knowledge

With olmalı, that inferential feeling becomes even stronger:

• eklemiş olmalı = he must have added it

In many contexts, -malı / -meli can express necessity:

• gitmeliyim = I should / must go

But in this sentence, olmalı is not about obligation. It expresses logical deduction:

• eklemiş olmalı = he must have added

So here must is not moral obligation. It is must in the sense of:

• That must be the explanation.

This use is very common in Turkish.

Here olmuş gives a sense like:

• it turned out a bit different
• it seems to have become a bit different
• the taste ended up a bit different

Again, -muş adds a nuance of observation, realization, or inference rather than a plain factual statement.

So:

• tadı biraz farklı oldu = its taste became a bit different / was a bit different
  
  • more plain, straightforward
• tadı biraz farklı olmuş = its taste has turned out a bit different / seems a bit different
  
  • more like the speaker is noticing the result now

That fits the context well: the speaker tastes it and notices that something is different.

tadı means its taste or the taste.

It comes from:

• tat = taste
• tadı = its taste / the taste of it

The -ı here is the third-person possessive suffix.

In Turkish, nouns like taste, color, name, smell, etc. are often expressed with this possessive structure when referring to something’s characteristic:

• rengi = its color
• kokusu = its smell
• adı = its name
• tadı = its taste

In full form, you could say:

• salatanın tadı = the salad’s taste

But Turkish often leaves the possessor understood from context, so just tadı is enough here.

Because Turkish often leaves out information that is already clear from context.

After hearing:

• Dayım salataya havuç ve mayonez eklemiş olmalı

it is obvious that tadı refers to the salad’s taste.

So instead of saying:

• salatanın tadı biraz farklı olmuş

the sentence simply says:

• tadı biraz farklı olmuş

This is very natural Turkish. The omitted possessor is understood automatically.

They are similar, but not always identical in tone.

• farklı = different
• değişik = different / unusual / altered

In food contexts:

• biraz farklı olmuş sounds fairly neutral: it tastes a bit different
• biraz değişik olmuş can sometimes sound slightly more marked, like it turned out kind of unusual

Depending on tone, either can be fine, but farklı is a very safe, neutral choice here.

The sentence is organized very naturally for Turkish:

• Dayım salataya havuç ve mayonez eklemiş olmalı,
• tadı biraz farklı olmuş.

The first clause gives the speaker’s conclusion. The second clause gives the evidence/result.

In English, we might more often say:

• The taste is a bit different, so my uncle must have added carrot and mayonnaise.

But Turkish is flexible, and here the speaker states the conclusion first, then follows it with the observation that supports it.

That order sounds natural and conversational.

Yes, that is a very good natural translation.

A few small nuance points:

• havuç is grammatically singular in Turkish, but English may prefer carrots in this kind of context.
• tadı biraz farklı olmuş is literally more like:
  • its taste has turned out a little different
  • the taste seems a little different
• But it tastes a little different is an excellent natural English rendering.

So your translation captures both the meaning and the tone well.

It is a fairly strong inference, not absolute certainty.

eklemiş olmalı suggests:

• I’m pretty sure this is what happened
• this is the most likely explanation

So it is stronger than a weak guess, but it still leaves room for uncertainty.

If the speaker knew for sure, Turkish would more likely use a more direct form such as:

• Dayım salataya havuç ve mayonez ekledi.

If the speaker wanted to sound less certain, they might say something like:

• eklemiş olabilir = he may/might have added

So eklemiş olmalı sits in the strong deduction range.