How does this antenna match work?
The only way I can see it working is if the lower impedance antenna (38 ohm) were connected to the "tap" of the auto transformer. A 38 ohm tap and a 50 ohm feedline means the tap is at 87% of the way up i.e. \$(0.87)^2 \times 50\Omega = \$ 37.8 ohms.

An 18 ohm tap is at 60% i.e. \$(0.60)^2 \times 50\Omega = \$ 18 ohms.

I can't see any other way round this other than the broadcast engineer got in a muddle or your ears need washing out LOL.

NB These calculations assume the auto transformer windings are 100% coupled to each other.