If you only ever want the fan on when the light is on that will work. If you want to control the fan separately you have to find a
12 volt source.
Not sure what your are saying when you say you cut 2 wires. The older roof fans were wired with a
12 volt source going to a switch in the vent cover. When the vent was opened the fan would come on some units had a switch second switch to be able to turn the fan off while the vent was open.
Test the red wires for voltage and wire the new fan to that assuming the new fan has some switching built into it. This will allow the new fan and or it's switch to control the fan.
As for the second red wire if you do not connect it I would assume some thing may no longer work. If you find something not working then you can decide if you want to connect it.