Yes, other controllers can interfere with your Wifi, however it's also easily mitigated. Let me explain the why and the how.
DJI Drones have auto channel selection. It does not matter if we are talking about a Tello (smallest) or the Mini or any bigger one, once you have the app set to auto select or auto detect it will choose one of the least congested channels to operate. This is how the theory works, when there are enough free channels.
Sometimes when I fly in the park, I fly with my son who is flying his Tello. It happened more than once that the Wi-Fi of the Tello does interfere with the Mini, however like
@Meta4 already explained, you can just move a couple meters away and the interference warning is gone. For us it happened in the 2.5 GHz band that both Mini and Tello have in common. If you want to make sure that you are not affected, you can always opt to manually choose a free channel.
Step 1: Enter DJI Fly APP main page.
Step 2: Go to the camera settings and click the three dots at the top right of the screen,
Step 3: Go to the "Transmission" tab and then to "Channel mode" select "Manual".
Step 4:You can choose the channel by touching the bar that you think is most suitable (it must be green and relatively high to ensure good reception).
Be aware that this only applies to the Remote Controller interference, once you fly away over houses there might be additional interference coming from there.