How to prevent ATTiny program from running after I flash it with Arduino?
This means that if I try to flash the program, ATTiny will start to put PWM power into my Arduino. I don't want that to happen.


Why do you think that is a problem? The "PWM power" cannot be any higher than the supply voltage, and that is 5V. The Arduino has no problem with you providing a 5V PWM signal to an input pin.

The only time it could be a problem is if the pin you are sending the PWM to is set to an output, in which case you could risk overloading the pin. To get around that you just need to insert a small resistor between the ATTiny's pin and the Arduino's pin. 330Ω or so should do it. Just enough to limit the current to a safe value (&lt; 20mA) but small enough that it won't interfere with the programming communication.

A well design schematic for an Arduino ICSP programmer would have had these resistors in all the data communication lines anyway.