You say you have three conductor wire going in and have drawn four. Something's amiss there. in 'standard' wiring, red is live, black is neutral, green is earth. Some schemes have brown live, blue neutral, green/yellow earth.
The light/fan fitting may not have an earth on it, hence the two conductors to the unit. If you want to separate the light and fan functions, you'll need to run another pair/triple. In a bathroom, you should have the fitting earthed.
Supply red (live) gets paralleled thru to the switches; black (neutral) and green (earth) gets joined to the corresponding colour to the appliance. The two reds go to their respective function on the appliance.
If you don't know what you're doing, get a licenced sparky to do the job. Particularly in a bathroom.
I wouldn't go jioning blacks and reds as in those diagrams. You may let a lot of smoke out of the system.

Use string. It's safer.