So technically, he was never acquitted of manslaughter. However (AFAIK), double jeopardy is supposed to prevent the prosecutor from trying lesser charges in subsequent trials until one finally sticks. The prosecutor is supposed to look at the evidence at hand and select the charge that fits the crime. The courts are not a buffet with a pile of clean plates for each trip.
If you read my post, it spells out what is a lesser, included crime and what is considered a separate crime.
The facts a prosecutor needs to prove for 2nd Degree Murder are exactly the same as they are for manslaughter except murder requires one additional element: malice. There are no elements for manslaughter that are not included in the murder charge.
Manslaughter is a subset of the facts for Murder, so if you acquit on Murder and charge manslaughter in the same trial, double jeopardy attaches to both charges.
Here's a better example of when they could refile:
Deedy kidnaps a woman, carjacks her vehicle in the process, and sexually assaults her.
The state can try him on kidnapping, grand theft auto and sexual assault charges in one trial. If he's acquitted of GTA and kidnapping, but the jury deadlocks on rape, the state can choose to refile the rape charge. Rape is not a "lesser charge" relating to GTA and kidnapping. It's a separate crime even though it was part of the same criminal course of conduct.
Manslaughter is a lesser charge of the same crime when also charging 2nd Degree Murder. So an acquittal for one is an acquittal for both.
That's my read on it. Based on what I've looked into, that's how double jeopardy protects us from being tried for 1st degree murder, then going through another trial for 2nd degree murder, and another trial for manslaughter, and another trial for aggravated assault, and so on. The Constitution protects us from prosecutors filing charge after charge for the same essential crime until they get a conviction.