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When I migrate to an external signal source, it begins to act wacky even though the clock domains are supposed to be synchronized since I'm using the Oven clock out from the signal source as my external clock source.
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Same clock source doesn't necessarily mean that the setup and hold times are kept for the external signal. It should be treated as unrelated in any case.
It's generally easy to get setup and hold timing conflicts with asynchronous inputs. I would try to avoid them. Otherwise, the output of the respective registers must be regarded unrelated to the system clock and must be synchronized anew.