I am not quite sure which Grammar book you are referring to but "Otherwise" has lots of meanings and can be used as an ordinary adverb, adjective or conjunction although this seems to be a British use. And according to Merriam Webster a Pronoun
"otherwise" is a conjunctive adverb and should be at the start of a sentence or after a semicolon,
This is a misconception
Like other adverbs, conjunctive adverbs may be moved around in the sentence or clause in which they appear.
However according to this source Ginger Software
Always use a period or semicolon before the conjunctive adverb when separating two independent clauses. Conjunctive adverbs are not strong enough to join independent clauses without supporting punctuation.
But according to this source Grammar Monster
Note that a conjunctive adverb is preceded by a semicolon when it joins two independent clauses but a period (full stop) when it joins two sentences.
Use a comma behind conjunctive adverbs when they appear at the beginning of a sentence’s second clause. The only exception to this rule is that no comma is necessary if the adverb is a single syllable.
Comma Splices When you want to join two independent clauses, you need a conjunction or a semicolon. A comma alone isn’t strong enough to join them. This kind of mistake is called a comma splice.
Following the above guidance notes;
I think staff should be paid commensurate with skills; otherwise, versatile employees can be headhunted by other companies such as international conglomerates.
I think; therefore, I am.
However "otherwise" is often used with conditional meanings similar to our case. I personally think that the use of just a comma is justified when we are joining what then becomes, in my opinion, an independent and a subordinate clause.
I think staff should be paid commensurate with skills, otherwise versatile employees can be headhunted by other companies such as international conglomerates.
We’d better send it express, otherwise it’ll take days. Ref C.E.D.