Am I properly using commas here?

I believe it is necessary. A good rule of thumb that I like to go by is if I were to remove whatever is between the two commas “, ,” then the sentence will still make sense. Observe:

The president states that he felt very disturbed.

As opposed to your sentence:

The president states that, after reading the memo, he felt very disturbed.

If there was just one comma (since this sentence is shorter in length) it would feel like there is an awkward pause before the description of how the president felt.