This is a Standard sentence Structure:
S + V(t) + DO + (ADV)
In your sentence, the personally qualifies the offence. i.e.
"He did not offend anyone on a personal level." This is not the same as "he did not offend anyone." They might have been offended professionally or on principle. (although those things are not necessarily implied)
By changing the position of the adverb, you are changing what is being modified by it, and thus the meaning. "He personally did not offend" implies that he offended over the phone, perhaps. That is "not in person."
He did not offend personally anyone is incorrect, as it rudely splits the Verb and the DO. "I like thankfully rainy days." It feels to me the same way a split infinitive feels. you might be able to set it apart with commas He did not offend, personally, anyone. But that leaves the meaning ambiguous (which might be good for humor)