Kohler use to have a tester for CDI ignition systems and a different one for non CDI ignition systems. I have found one source that shows the 25 455 01 for non CDI systems and another source saying that the 25 455 01 is used with all ignition systems. and both are Kohler sources. The CDI Kohler test that I have says HEI on it. And they always said that if you use the wrong tester it will give a false positive.
It does appear that Kohler has discontinued the HEI tester so it looks like you have the correct tester. It looks like the current version of the one that I have is this one
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