This is a complex issue. As we know analysis of kamma is one of the “unthinkables” (acinteyya). What that means is a human (other than a Buddha) will never be able to COMPLETELY sort out what happens in a given situation. But we can understand general trends.
Only clear-cut is an anantariya kamma vipaka. That will bring vipaka before any other pending vipaka.
Other than those, there could be many factors coming into play at the cuti-patisandhi moment. But if one of the strong vipaka is clearly stronger, it will come to the front. But if there are several vipaka of about the same “magnitude”, that is when the state of the mind could play a role.
The other KEY POINT to remember is that grasping a new bhava is NOT done CONSCIOUSLY. It is automatic, based on those and possibly other factors. It happens naturally, just like many things in the nature just happen according to nature’s laws.
For example, when a reservoir starts overflowing, the water will go over the lowest point of the wall holding the water, if the height of the wall is not the same. Or, in a hurricane, while those trees with weak roots could be uprooted, one’s with strong roots will survive. It just happens, based on many factors at play (strength of the winds, weakness of roots, whether a tree a shielded by other trees, etc).