Does the target of dominate person receive an initial save?
Compelling Domination (Su)
When a seraptis uses dominate person, its victims do not actively resist and never gain a new saving throw when ordered to take actions against their nature
The wording is somewhat vague but since the statblock lists a DC, I believe the intention is that they receive their initial save versus Dominate Person.
They definitely receive their initial save. They only don't receive subsequent saves for the specified reason. If they get a subsequent save for a different reason (spell, class ability, etc.) they still would roll again.