Not always, Immortality doesn't mean they Stop aging
I Play Vampires as demonic figures, creatures of immense darkness.
My Daemon is Named Daerick, He was born in the 6th Century, he wasn't always a daemon tho, he was a Sorcerer along with twin Brother Kaegan. It's a Long and dark History, essentially Kaegan is responsible for turning his brother into a daemon, and he was his burden. Until Daegan's Darkness was too much for their world, and Kaegan banished him to the Realm of Darkness, the perfect prison.
It depends on the supernatural,
For Daegan He's also a sort of incubi. for Centuries he manages to break free from the realm of darkness temporarily, and have an affairs with a willing victims. The plan was to plant his seed and bring daemon pawns into the world, that would help him with his plan.
In the Middle ages -High Middle Ages, Daegan obtains 10 victims to carry his spawns. He Impregnates 7 Knights one of them twice, 3 of the 7 Knights were of the King's Royal Guard, he takes The Queen, and finally the King Himself.
In 1868, a victim whom he did not intend to genuinely fall in love with, it almost came to the point where he was so in love with Regina, he was about to Abandon his designs for revenge. That was until his lover was murdered.
It's all about the relevance of Age, Even in my soon to be Sorcerer HouseHold
We have Kaegan a Sorcerer who is essentially over 1500+ years old, but biologically he looks 45, he has appeared to be in his late 30s-40s for the last 500 years.
Remember Daegan is Kaegan's twin, so he's just as old, also biologically 45 years of age.
Kaegan has a Daughter with his wife Vivian, Julia, was born in the late 1400s. Almost 500 years pass and it's the 1980s, and Julia biologically appears to be in her mid-twenties. when She meets her Husband. and has kids. Her kids will inherit a regular Human aging.
For all the Daemon spawns Daegan Created, One who was born in the medieval ages, is almost taken out of time. "Put on the shelf, until Daegan is ready to put him into play, and doesn't until Julia's Son, Kaegan's Grandson, and Daegan's Grand-nephew is Born, in the early 2000s. As they continue to grow up. You won't biologically notice who is older, yes, my point is when it appears, that a Immortal "eternally young" vampire has a kid and that kid grows up to appear the same age as their parent. Just remember how long their parent has been around before their kid.