Yes you are killing your Rosemary with kindness in their native habitat the soil is poor, rocky and on the dry side.

Do feed Basil, and--to a lesser extent--Mint, Cilantro, and Lemon Balm. Almost all other herbs like to be on a strict diet, though herbs in containers need at least a litle fertilizer, since the nutrients leach out faster in pots.

Mint in my experience needs no fertiliser, grows fast enough without!

True, but it can still get yellow and mangy in a container if it doesn't get some food. I do tend to use something mild and slow acting, such as alfalfa meal.

Ah your climate is rather different than ours... mint is almost a weed in some folks gardens.

Chatbud your Rosemary will need a lot of water in Singapore.

It is also not going to be happy about the hot nights and humidity, there. Rosemary tends to get a little wimpy here during our monsoon season--ditto garden sage, some oreganos, and lavenders

The checks that I did seem to imply that Rosemary can cope with humidity - if so it does better than me!

In my experience, the problem is a combination of humidity, 35º+ nights, and 40º+ days. I don't know exactly how hot Singapore gets in the summer, but I'm sure that it is a lot more humid than we are, even during our monsoon season. In its native habitat, Rosemary experiences sunny, dry, moderately hot (30º-33º daytime) summers.