OK the wires in the switch box are all hot or switched hot (plus the bare gnd). The white wire in this box goes to both switches (can see but think so) and so is the always hot. (So don't think it is a neutral; there is no neutral in the switch box.) The black and the red are switched hots for the fan and light.
Look in the box for the fan and find the cable from the switch box--it will have the black, red, and white wires in one cable. The red wire will be connected to the blue for light and the black wire to the black fan wire. The white wire is being used for hot feed and it must be connected to an always hot, which will probably be one of the other black wires. You must determine this by testing voltage with switches off and on. You should mark the ends of this white wire with black tape to indicate it is a hot.
The other two white wires (joined) are neutrals (one from the feed and one to the other fan) and these two wires are to be connected to the white lead (common neutral) of the fan/light.
The striped green is ground for the fan/light and should be connected to the bare copper ground. The green from the box must also be a ground to the box and it is to be connected to the bare copper ground.
The final black wire must be the hot feed to the other fan. If we have this straight, then it should be connected with the black marked white.