Why were supposedly more or too many contacts detected and billed?

Only the contacts actually kept in sync between source and destination are counted as "Synchronized contacts" (see "My connections").

You can find more detailed information about how many contacts were detected in source and destination in the synchronization log (My Connections -> Actions -> Download Sync Log). 

Example:

2022-09-01 07:32:35,378 (App1/Microsoft)(contact) Processing raw objects
2022-09-01 07:32:36,092 Found 5139 objects