Nothing triggers it. It’s just one of the 6 possible and equally correct ways of expressing the same thing.
There are 3 things you have to keep in mind about a Tagalog noun and its modifier/adjective. These are:
1. In practically all cases the positions of the noun and its modifier are interchangeable.
2. The linker “na” is needed to associate the modifier or modifiers (normally, not to exceed 2) to the noun.
3. Whenever possible, the linker “na” is usually attached to the preceding word.
For example:
(favorite sport/game) paborito NA laro = paboritoNG laro; laro NA paborito = laroNG paborito
(fragrant soap) sabon NA mabango = sabonG mabango; mabango NA sabon = mabangoNG sabon
The Tagalog possessive pronouns become adjective pronouns when the “na” is attached to their endings.
Possessive pronoun >> Adjective pronouns/Possessive adjectives
Akin (mine) >> Akin NA = AkinG (my) – when not in the initial position, “aking” becomes “ko”.
Iyo (yours) >> Iyo NA = IyoNG (your) – when not in the initial position, “iyong” becomes “mo”.
Kaniya (his/hers) >> Kaniya NA = KaniyaNG (his/her/its) … “kaniyang” becomes “niya”.
Amin (ours) >> Amin NA = AminG (our) … “aming” becomes “namin”.
Atin (ours) >> Atin NA = AtinG (our) … “ating” becomes “natin”.
Inyo (yours) >> Inyo NA = InyoNG (your) … “inyong” becomes “ninyo”
Kanila (theirs) >> Kanila NA = KanilaNG (their) … “kanilang” becomes “nila”
For example:
ang AKING laro = ang laro KO
ang KANIYANG kotse = ang kotse NIYA
ang INYONG bahay = ang bahay NINYO
However, there are a few times when we would retain the “possessive pronoun + na” after the noun. It’s when we want to emphasize ownership. It is similar, for example, to how “mine” might be used instead of “my”.
MY book = Ang AKING libro = Ang libro KO.
The book is MINE = Ang libro ay SA AKIN. - Emphasis on ownership.
In the phrase that you gave, “isa sa mga paborito kong laro”, the noun (N) is “laro” and it has 2 modifiers – (M1) “aking/ko (my)” and (M2) “paborito (favorite)”. With these 3 elements, there are 6 (or 7) possible permutations/arrangements that can be made with them. These are listed below, together with their linkers.
1. M1-M2-N: akin NA paborito NA laro >> akinG paboritoNG laro
2. M1-N-M2: akin NA laro NA paborito >> akinG laroNG paborito
3a. N-M1-M2: laro NA akin NA paborito >> laroNG akiNG paborito
3b. N-M1-M2: laro NA AKIN NA paborito = laro KO NA paborito >> laro KONG paborito (pls. refer to pronoun transformations above)
4. N-M2-M1: laro NA paborito NA AKIN >> laroNG paborito KO
5. M2-M1-N: paborito NA AKIN NA laro = paborito KO NA laro >> paborito KONG laro
6. M2-N-M1: paborito NA laro NA AKIN >> paboritoNG laro KO
So, if you’d append any of the 6 or 7 arrangements above after “isa sa mga”, they would all sound equally correct. Your phrase is just one of them, the 5th arrangement above.
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Clarifications on what you mentioned in your post.
No question there: It's either the "sa" pronoun in front or the "ng" one in the back.
“Sa” is a multi-purpose Tagalog preposition. When used before a noun, its English translation could vary. For example: “SA mga laro ko...” = IN my games...; “SA mesa” = ON the table; “SA pinto” = AT the door. When used after a verb, its more common translation is the preposition “TO” or "FROM, e.g., "ibinigay SA iyo" = given TO you, "kinuha SA iyo" = taken FROM you.
“Sa” functions independently of the “ng” ending of the possessive pronoun that might follow it.
But sometimes, the "ng" pronoun is used in front - for instance, "one of my favorite games"
"Ng" is not a pronoun. It is either the linker "na" when it gets attached at the end of a word ending in a vowel or the preposition "of" when it stands alone, e.g., "Isa SA mga laro ko" = One OF my games.
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