I would be curious to know the make and type of the safety tester you are using, any of the high voltage testers that I have used at 5kV are battery operated and have the same rating for both test leads. At higher voltages and mains operated, there can be different types of leads for the +ve and -Ve connections.
A lead in itself, does not have a CAT rating, that is the rating of the input of the tester that has the capability to read up to 600V / 1000V, to warn against an energised circuit.
The output of the test set will be isolated, so the potential difference can only be seen across the red and black lead, so in the event of your scenario, the black lead only sees 5kV with respect to the red lead, that is rated at 10kV insulation.
If you connected the test set up with +ve to the chassis of the DUT and the -ve to the winding, then under your scenario, the black lead could be stressed. That is why high voltage test engineers are careful about how they place the test leads and connect to the DUT, to ensure that there is little risk of leakage between leads. The guard terminal on the tester can also be utilised to avoid issues with current leakage.
Depending on the type of test set, the output current will be limited to some extent, generally maximum of 15mA, but usually much lower for battery operated instrument. When the current goes above this, the output voltage of the tester will drop, so there is a low risk to personnel carrying out the test.
The situation you have presented would also be due to poor working practices. In industrial environments where these kind of testers are utilised, there will be strict control measures in place for carrying out this kind of testing, and one of those will be inspection of the test apparatus prior to carrying out the test.
High voltage testing of any kind will always carry certain risks with it. That is why the test engineers are specifically trained and follow strict working practices.
Kind regards.