The only thought I have is that it might be worth checking whether it matters how you select the item. If, for example, you usually select the desired item using the Return key, get into the habit, for a while (however many days you feel necessary to test), of using a mouse click instead. If the problem does not reoccur over the test period, that would suggest that the trigger method is relevant.
Alternatively, go straight to checking through your KM macros (and any other automation you have set up) whether your usual selection method (such as using Return) could be triggering some other macro or interaction, which is what I am getting at by suggesting the above test.
It's a double click that is betraying me. If I go down the list and double click it pastes the item that is currently at the top of the list. In addition the item that I double clicked on now moves to the top of the list. Given that I'm looking for a psychotherapist right now, we could start making jokes that double clicking in KM has sent me to therapy ;-).
If Safari is caching the clipboard and not noticing the change before pasting, that would be sad.
That said, it's possible the issue is with the web page and how it behaves.
I'm afraid there isn't anything I can do, the behaviour from Keyboard Maestro Engine is essentially:
Set the clipboard
Simulate Command-V.
Setting the clipboard is a synchronous action - that is, the clipboard is set in to the system clipboard at the time, there is no delay in it happening.
Simulating a key on the other hand is a queue action, and so the key is added to the queue and at some later time the application asks for the next key, and gets the Command-V and hands that to the system to activate the appropriate menu, in this case Paste (or possibly the web page intercepts the Command-V and does whatever it feels like - and this could be affected by extensions you have installed).
So there isn't any realistic way for the previous value of the clipboard to be pasted except by something somewhere caching it.