"When you have to turn off Twitter because the president can't spell and Russian bots are spamming you 24/7. At least he fixed it," the web designer tweeted on Friday.
The tweet has gathered more than 1,000 likes and 300 retweets.
Alex, from Los Angeles, told PEOPLE he woke up on Friday to several hundred notifications on his phone. While he's used to this happening whenever Baldwin is in the news, this time many of the messages seemed to be coming from bots.
"They don't make any sense and you can tell they've just been stuffed with keywords and are programmed to generate from whatever tweet is trending at the moment," he told PEOPLE.
Alex replied to a tweet in which Alec said he would like to "hang in there for the impeachments hearings, the resignation speech and the farewell helicopter ride to Mar-A-Lago".
"Let's get a drink when this is all over," Alex said.
He seems to have even changed his Twitter bio after the incident, which makes a reference to Trump's misspelling of the word 'dying' as he attacked the actor's career.
It reads: "Dieing mediocre career. No relation to @ABFalecbaldwin".
He has also asked Twitter to 'please help' him by verifying his account, tweeting: "@TwitterSupport it's been a hell of a day, can you verify me now that I'm trending?"