Just submit a complaint with justification via their web portal / email / walk-in-counter. Provide all the exact details, e.g. your house address, name, contact, location of tree (front/back/side/etc.). Check the drain if it cracks/damaged as well. Can submit as complain for them to fix it in future as well. Also take note of your water piping from meter-underground garden-house if it is affected/leaking from the tree roots as well.

Depending on how efficient is your local council MPSA when they will come over to cut it or need to follow up. My case with DBKL they do not respond anything, they just come quietly and cut it down one fine day within a week.

Also, you do not need to pay anything to anyone. In case some sub-con or scammer tries to extort money from you. The fees already included in your cukai pintu.

I assume the tree is outside your house compound or fence. If the tree is inside your fence in your garden, then is consider your own property and you need to pay contractor to cut it down.

Read again I did not mention anything about claiming damage from MBSA. That is another different story with many arguments. What I mention is to request chop down the tree if it belongs within the local council jurisdiction. Any other damage inside/outside the fence is subjective on a case by case basis.

I'm not a tree expert. It doesn't have to be very special tree that stood out like a sore thumb for local council to identify. Normally developers will plant only 1-2 types of tall/big trees along all the same roads in each development phase. The local council can just browse along the road or next road and can get an idea already. Although some very old housing estates may have mixed trees.

So, unless it really stood out, normally local council will just cut it down for you. Like my friend having a palm tree (special mah when plant it ) which stood out like a sore thumb and grow over two storey high, have to fork out own money >1k to get it chop down.
Another friend had a dying old nangka tree without much leaves/branches left and no fruit, manage to get local council to chop it down since it doesn't look too special.