You're a clinic vet. You have set hours.
If there were an emergency, they'd call the emergency vet clinic, stop acting like your job is a specialized emergency surgeon or an emergency on call doctor.
Even if you were an emergency vet there would be on and off days. You're not on call 24/7. You work with at least 6 other people.
When you're off hours, you're off.
Jesus Christ.
They need to talk. Minato needs to get his jealousy under control, but the BF needs to set boundaries at work.