Field mappings and transforms run every time. They will add a work note on the parent record at minimum even if "Sync when" is set to "Never".
A 'Sync when' value of 'Insert' or 'Insert or Update' is when the parent record fields get updated for the mappings.
"Sync when suggestion" is what the Provider sets when creating a RTD mapping. The consumer can override this setting which is the "Sync when" field on the RTD mapping in the consumer.
Virtual fields only sync if an actual mapped field is updated. On insert all values are sent. If a virtual field is updated the value will not sync unless a mapped field has also been updated.
There is an api which can be used to trigger virtual field update but Doc site is currently down. I will update with link when available.
