I have a similar Fleischmann turntable(TT), though I'm not sure of the Catalogue number and know nothing of the three rail element.
Initially I did not fully understand the current flows and functionality regarding polarity, but eventually found the following :-
a) You need to check that the 4 sprung contacts on the TT Deck track ends are not distorted , damaged or missing. These need to be 'true' to make contact with the outlet tracks when you 'park' the deck in order to pass the current from deck to outlet track.
Remove outlet tracks or 'blanks' from the well at any position to enable the deck to be removed and examined.
b) On my example, when the deck rotates it will pass a point *halfway round the circumference where polarity is reversed, so I found it necessary to fit a Double Poll Double Throw (DPDT) switch to have control over polarity. This may be why you are experiencing 'shorts' when a loco has been turned and the polarity has become opposite to that of the running line onto which it is exiting the TT.
* This halfway point may not be obvious and depends on the original orientation of the TT Deck when first installed.
Regarding the 'Hut' position on the rotary switch, this enables a loco to be parked on the TT Deck while other models on the running lines are operated from the same controller power feed if desired. So, if you wish to drive a loco on or off the TT, the Hut or No Hut switch is selected for the Deck outlet to the running line depending on which end of the deck is connecting. Changing the rotary switch then isolates the loco on the TT .
Hope this helps,
Regards,
John