Manilkara bidentata (A.DC.) A.Chev., Rev. Bot. Appl. Agric. Trop. 12: 270 1932. (Syn: Mimusops bidentata A.DC.); 
Trop. America as per WCSP;
I am not sure about this plant, by first look, it is looking like some Sapotaceae members. But fruits looks like Calophyllum inophyllum, it has axillary raceme inflorescence. In this plant, it has axillary fascicaled or subfascicaled inflorescence.

From your hint and googling I see Manilkara bidentata as a close match

Check Clusia rosea- Autograph tree

It cannot be Clusia rosea- Autograph tree. I have wonderful photos of autograph tree  taken in Chennai. I go with the ID of …

I too agree with … Fruits looks like Calophyllum sp

for me it looks like manilkara kauki (L.) Dubard

for me too it looks like C.inophyllum

It is definitely not Calophyllum inophyllum as the flowers do not match at all.
More likely to be a Manilkara sp.

I still believe it is Manilkara bidentata, … was also thinks its most likely.
kauki has a much darker bark, and fruits are not round at all.

… is correct. Though the fruit can be mistaken for C.inophyllum, looking at the floral buds, foliage the tree could be Manilkara bidentata only.

Manilkara bidentata only. The fruits are either globose or oblate. Agree with M. bidentata, commonly known as Bullet Tree native of America?