I remember there was such issue in OG MS that if you job adv your mage after level 8 or your warrior after level 10 by mistake because of quest completion EXP (or any other reason) you would lose your MP/HP growth because of the skills you level up at 1st job effect only when you level up and not retroactively. They did fix it in GMS eventually. What happened to me is that I didn't know that the job adv gives 300 exp and gained more exp at level 10 with my warrior, causing me to level up to the job adv. Did I lose HP?
Those skills generally take a few SP to unlock anyways, so no you didn't lose any. And one level worth of them won't make a big difference anyways, it's tiny when you consider you'll be getting the full bonus for almost 200 levels
So I see it's still a thing. Luckily after opening this thread I figured out what you said myself about the amount of SP required to unlock these skills so for warriors you start to lose HP if you for some reason did not job adv until level 13. By the way, the approach back in the day was way harsher, people would literally reset their hard worked on characters even at 3X because of such mistake.