If you are splitting air output from one air pump to 2 separate tanks, you need to install a flow control valve on one or both of the lines, so that you can regulate and balance the air output between the 2 tanks.
Air travels via the least resistance, thats is why you see the air bubbles coming out of the tubing with cuts (has least resistance), whereas the air stone got no bubbles (the air stone pores are denser and hence higher resistance). Adjusting the air flow on one or both air lines will solve your issue.
Here is a photo of a flow control valve (there are plastic versions too):
This is a multi-port flow control valve so you can adjust air flow for more lines:
Photos from Google Images.
Also remember to install a check-valve along the lines if you are placing the air pump below the tank water level.
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