Twitter has long done this, showing 'popular' tweets instead of the latest stuff. This is a terrible way to experience Twitter. Now you can (finally) arrange tweets chronologically.
This is a relatively new feature for both iOS and Android, but at this point it should be available to everyone. For simplicity, the process is identical on both platforms. Here's the skinny.
If your Twitter is open on your timeline, look in the upper right corner. There should be a small star symbol. Tap that thing!
A new menu opens, displaying the "Show Recent Tweets Instead" option. Tap magical, automatic and some other "cally". Get your tweets in chronological order. The tastiest way to consume Twitter.
If you're fed up with seeing things in a meaningful way, you can also use the Twitter curated method. Tap the small star icon again and choose the somewhat neatly named "Go back Home" option.
And just like that, your tweets are back in the right order making little or no sense.