OK, that's prompted me to do the actual figures.
Let's assume the two snapshots of the POTUS account were taken at the same time of day, and take the rounded numbers of followers, 18 million and 18.2 million, as exact (they're not).
An increase of 200,000 followers over 3 days means an extra 66,667 followers a day. That's 2778 new followers an hour. Or 46 new followers a minute.
Making the same assumptions, the @ realDonaldTrump account gained a new 300,000 followers over 3 days. Ie 100,000 followers a day, or 4167 an hour, or 69 a minute.
So although going on Buzzfeed's numbers, the first tweet Buzzfeed examines is clearly false (there aren't 5 million new followers), the second has every chance of being true (new followers won't arrive evenly, so it's entirely likely there were periods when the rate of new followers was 100 a minute).
30 May was the 130th day of the presidency, so if the @ realDonaldTrump account had been acquiring new followers at the rate of 100,000 a day since 20 January (and none had unfollowed him), the account would have 13 more million followers on 30 May than on 20 Jan. I don't if this matches what's actually been seen.
(There's substantial room for error because of the rounding to the nearest 100,000 in Twitter's numbers, but I'm too lazy to work out the margins. However even if rounding has overstated the increase in followers, it remains entirely likely that there were periods of 100 new followers a minute.)