That's the correct indication for the transformer in its original configuration.
With a normal outlet, the neutral and the ground are bonded together at the service entrance, so the tester will light two lights: one between line and neutral and the other between line and ground, since the same voltage appears across both pairings.
With the tester plugged into the transformer, there's voltage between line and neutral created by the transformer secondary, but now there's no path between your isolated neutral and ground, so now that light on the tester no longer lights, indicating "open ground".
It sounds like you're talking about an oscilloscope or something similar. In that case, the channel-to-channel isolation describes the isolation between each channel and every other channel. The channel-to-ground isolation describes the isolation between each channel and ground. These are different, but related, concerns.
Channel-to-channel isolation describes how much voltage differential there can be between two inputs to the scope.
Channel-to-ground isolation describes how much voltage there can be between any input and the ground input to the scope, usually through the power connector.
The "techniques" involved aren't different at all. When two things are to be isolated, make sure there aren't any conductive paths between them, and make sure that all barriers between them (optocouplers, transformers, air distance, creepage distance, insulation, etc.) are rated for the isolation voltage you want.
Now, if all channels are isolated from each other, they must also all be isolated from ground; if they were all referenced to ground, they would all also be referenced to each other! It is, however, possible to have all channels isolated from ground while still being referenced to some other common node. This scenario can be useful, depending entirely on what it is you want to measure. If all the signals being measured are referenced to the same voltage, which is not earth, then your scope also having isolation to ground but not channel-to-channel would be fine.
As for crosstalk, that would require more details about what you're doing. I don't think there's a general answer there.
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Functionally though, having isolated I/O means that if something goes horribly wrong in the field with your I/O wiring and wires get crossed up, you might damage that particular I/O point, but it will not go further into the PLC and fry the whole thing. it's easy to replace one I/O card, it's not easy to replace an entire PLC.