Despite him turning into Buddy several more times, there's no mention of him ever changing into a monster again first. When he first takes the formula he falls unconscious and several seconds pass before he wakes up now horribly deformed. The entire segment is actually a nightmare Julius is having of the formula failing, while in the real world, it's turning him into Buddy Love.
WMG / The Nutty Professor (1963)
In the animated sequel to the original Nutty Professor. The universe was transformed into a comupter animated world because of an experiment gone wrong accidentally caused by Julius Kelp.
The scene in the original where Dr. Kelp becomes a monster before he turns into Buddy Love is actually a fever-induced dream in Julius's head.