IMO, both are correct and the meaning would depend on the
emphasis of either phone-calls or business-hours.

I will make phone calls only after business hours OR

The above can be interpreted as "I will make phone calls only after
business hours. During business hours, I will do something else".
The emphasis here is on "business hours" and what one will do during
and after business hours.

I will only make phone calls after business hours

Here, the emphasis is on phone calls. It can be interpreted as "I will
only make phone calls after business hours. I will not do email
after business hours"

Thoughts ?

I found a grammar web site that it discusses the placement related to what kidn of adverb, so it could be at the beg. middle or end. Confussing to learn all these rule. I agree with the empahsis type of explanation.

Grammatically they are both correct. This is one of those subtleties of language. MGMAT SC has a page or two on it. They mean different things, so if this were being tested on the exam it would depend on what they were trying to say in the sentence.

As Jay said depends on what you are emphasizing.