Çayı dökünce masa örtüsüne biraz çay bulaştı.

Because çayı is çay + the definite/direct object ending.

• çay = tea
• çayı = the tea (as the thing being spilled)

In Turkish, when a direct object is specific/definite, it usually takes the accusative ending. Here, the speaker means a particular tea that got spilled, not tea in general.

Also notice the buffer consonant -y-:

• çay + ı would be awkward, so Turkish uses çay + y + ı = çayı

So Çayı dökünce means something like when/after spilling the tea.

This ending often means when, once, or after doing something, depending on context.

• dökmek = to spill / to pour
• dök-ünce = when/after (someone) spilled it

So:

• Çayı dökünce... = When/After spilling the tea...

The form changes by vowel harmony:

• -ınca
• -ince
• -unca
• -ünce

Since the verb stem here has ö / ü-type vowels, you get -ünce.

The base verb is dökmek (to spill / to pour).
When suffixes are added, the stem can appear as dök-.

So:

• dökmek → stem dök-
• dök + ünce → dökünce

This form does not show person by itself. The subject is understood from context.

In a sentence like this, Çayı dökünce..., the understood subject is usually he/she/they or I/you, depending on the larger context. Turkish often leaves subjects unstated when they are clear or unimportant.

By default, yes, learners often understand it as the same subject context, unless the sentence clearly shows otherwise.

However, in this sentence, the more important point is that dökünce is a subordinate clause meaning when/after spilling the tea. Turkish often leaves the doer unstated.

The main clause is:

• masa örtüsüne biraz çay bulaştı = some tea got on the tablecloth

Here, biraz çay is the grammatical subject of bulaştı.

So the structure is roughly:

• Çayı dökünce = when the tea was spilled / when someone spilled the tea
• masa örtüsüne biraz çay bulaştı = some tea got onto the tablecloth

English may prefer different wording, but Turkish does not need to state every subject explicitly.

Because it has the dative ending, meaning to / onto.

Breakdown:

• masa = table
• örtü = cover, cloth
• masa örtüsü = tablecloth

Then:

• masa örtüsü + ne → masa örtüsüne

Why -ne?

1. The noun already ends in a vowel-like possessive form -sü
2. Turkish inserts -n- before some case endings after 3rd-person possessive forms
3. Then the dative ending is -e / -a

So:

• masa örtüsü = tablecloth
• masa örtüsüne = to/onto the tablecloth

Turkish compound nouns often use a special construction where the second noun takes a 3rd-person possessive-looking ending.

So:

• masa = table
• örtü = cover/cloth
• masa örtüsü = table cover / tablecloth

This is a very common Turkish noun-compound pattern. Even though it looks possessive, in English it is often translated simply as a compound noun:

• otobüs durağı = bus stop
• yatak odası = bedroom
• masa örtüsü = tablecloth

So yes, it means just tablecloth, even though the form is more literally something like table’s cover.

Because biraz çay is indefinite/non-specific here: some tea.

• biraz = a little, some
• biraz çay = some tea

Turkish usually does not use the accusative ending on indefinite nouns used this way.

Also, in this sentence biraz çay is the thing that got onto the tablecloth, so it functions as the subject of bulaştı, not as a direct object.

So:

• çayı = the tea (specific direct object in the first clause)
• biraz çay = some tea (indefinite subject in the second clause)

bulaşmak means something like:

• to get on
• to smear onto
• to stain
• to rub off onto
• to become transferred onto something

So biraz çay bulaştı means:

• some tea got on
• some tea stained
• some tea was transferred onto

In this sentence:

• masa örtüsüne biraz çay bulaştı = some tea got onto the tablecloth

This verb is commonly used when a substance accidentally gets onto a surface, piece of clothing, hands, etc.

Examples:

• Gömleğime yağ bulaştı. = Oil got on my shirt.
• Halıya kahve bulaştı. = Coffee got on the carpet.

Yes. bulaşmak commonly goes with the dative case for the thing that receives the stain/substance.

So:

• masa örtüsüne = onto the tablecloth
• gömleğime = onto my shirt
• eline = onto his/her hand

Pattern:

• X, Y’ye bulaştı = X got onto Y

In this sentence:

• biraz çay = the substance
• masa örtüsüne = the surface/item it got onto

In Turkish, biraz çay is treated as a singular idea here: a little/some tea.

The verb agrees naturally with that subject:

• biraz çay bulaştı = some tea got on it

This is very normal in Turkish. English also often treats mass nouns similarly:

• Some tea spilled
• Some water got on the floor

So bulaştı being singular is exactly what you would expect.

Because the two clauses are doing different jobs.

1. Çayı dökünce
   Here çayı is the specific tea that was spilled.

2. masa örtüsüne biraz çay bulaştı
   Here biraz çay refers to some amount of tea that ended up on the tablecloth.

English might also repeat it:

• When the tea was spilled, some tea got on the tablecloth.

So the repetition is natural because:

• first clause = the spilling event
• second clause = the result of that event

It can mean both, depending on context.

• çayı dökmek can mean to pour the tea
• but in a context like this, where tea ends up on the tablecloth, it is understood as to spill the tea

So context tells you which English verb fits best.

That is very common in Turkish: one verb may cover meanings that English separates.

Yes. Turkish word order is flexible, although the given version sounds natural.

Current sentence:

• Çayı dökünce masa örtüsüne biraz çay bulaştı.

You could also hear variations depending on emphasis, such as:

• Çayı dökünce biraz çay masa örtüsüne bulaştı.

The meaning stays basically the same, but the focus shifts slightly.

In Turkish, the element just before the verb often gets extra emphasis, and sentence order can be adjusted for information flow more freely than in English.

A few things may help:

• ç is like ch in chair
• ö is like the German/French-style front rounded vowel; there is no exact standard English equivalent
• ü is also a front rounded vowel, again not a normal English vowel
• ş is like sh
• ı is the dotless i, a vowel somewhat like a relaxed sound in the back/center of the mouth

So:

• çayı ≈ cha-yuh / cha-yı
• dökünce ≈ dö-kün-je (with c in Turkish pronounced like English j)
• örtüsüne ≈ ör-tü-sü-ne
• bulaştı ≈ bu-lash-tı

Also remember:

• Turkish spelling is very regular
• each written vowel is pronounced clearly
• stress can vary, but for a learner, clear vowels matter more than perfect stress at first