It seems I have missed some action here.
@Character 1: There could be several reasons for your motorcycle stalling during rains (we are not including the issues that could occur in ANY season, hence specifically focusing on what could go wrong during rains):
1. Water in fuel or fuel delivery system: Since you have cleaned your fuel tank (I hope it has been done properly), I can think of the following things:
a. Check the fuel flap. Does it shut properly? If there is a gap between its mouth and the rim of the fuel tank, water can still enter the fuel tank.
b. Check the fuel tap. Do you see any brownish/pinkish deposits on/around it? If yes, then its a sure sign of petrol leakage. If petrol can come out, water could also go in. Get it replaced.
c. Check the fuel line. This is the pipe running from the fuel tap to the carburettor. If you find any cracks or leakage, replace it.
d. Check the carburettor. As Anand has correctly said, start by draining the float bowl. It will generally be the lowermost screw that you will see on the carburettor but still, please post a picture of the carb from both sides and I will mark the screw that you have to unscrew. If all this sounds Greek to you, ask any roadside mechanic to drain the 'float' of the carb. Dont pay him more than 10 Rs for this. Second point: do you see small pipe connected to the carburettor and hanging loosely at the other end (see picture)? If that 'other end' is hanging too close to the road, then it would get clogged due to slush and grime and would choke the carb due to which the engine would sputter and die. Clean it, route it properly, and refit.
e. Check the air filter: 5 minute job. If you find any moisture there, replace it immediately. Also check the air intake and the hose that connects the air filter to the carburettor. If you see and cracks, replace it. Check the circlip that connects the hose to the carburettor. If its loose, tighten it.
2. Moisture in the electrical system: Understand how your Twister's ignition system works. The push button starter generates current from the battery which goes to the ignition coil where it gets multiplied several times. This current is sent to the spark plug that generates a spark to ignite the air-fuel mixture supplied to the combustion chamber by the carburettor. If there is something short in this electrical system (maybe due to moisture), the supply of current would terminate and the motorcycle would stall. I can go on and on on this but to keep it simple, please do the following:
i. Blow air into the ignition key slot and on handlebar switches. Open the switches and see if there is any moisture inside. Replace them in case there is moisture.
ii. Check the ignition coil, especially at the connector and look for any moisture. Wipe it with a clean, dry cloth and reconnect everything tightly.
iii. Check all wires, fasteners, and connectors. Insulate properly what you find exposed and secure all connectors properly and tightly. No problem in using insulating tape on the connectors.
iv. Replace the spark plug just for the heck of it and see if it makes a difference. Costs less than Rs. 100 and would not go waste as it can be used later.
v. Check the spark plug cap for any corrosion/cracks/moisture. Replace it if you find anything wrong.
Hopefully the above would solve your problem. Anyways, cheer up- July is over!