simple circuit review
Yes, I think your problem is that when the TIP is not conducting, there is a current path from the 12V through the fan and the custom board / LCD to the 5V of the Pi. The custom board / LCD is reverse powered, and the Pi might receive more than 5V (in which case the 5V has more than 5V at its output). Not good!

A simple solution would be a diode in the line from the Pi to the custom board, but note that your are switching the 5V with the TIP, which will already cause a significant drop in the voltage. This might be a problem for your custom board / LCD. It is less likely to be a problem for the fan. Adding another diode drop might not be a good idea.

Another solution would be to use two separate TIP's to switch the fan and the LCD.

IMO the only real solution is to switch in the power line(s) instead of the in the ground. Assuming your custom board / LCD draws little power from the 5V I would add a 5V linear reguator and power both that regulator and the fan from a switched 12V. 

Two quick grabs from searching "high side switch":