The first sentence is correct. I am not sure if your friend missed using an 'I', like ".....after I found that....."

after finding out

This is correct because "finding out" is an event (a noun, more or less) based on "finding" (with '-ing') being a gerund, or "verbal noun", and therefore doesn't need to be a verb with a subject.

But, "found" is not a gerund, so it behaves like any other verb; it needs a subject. In order to be correct, "after found out" would need to be something like "after I found out".

Both of these would be correct:

Unchanged:

1. I did some research of my own after finding out that he used to be an artist.

Corrected:

2. I did some research of my own after I found out that he used to be a renowned artist.

On your friend's correction:

Because you are describing events of the past already, you don't need to have every single verb everywhere to be in the past tense for us to know it happened in the past. Gerunds are allowed when narrating a past event.