You can set them up various different ways over at paper.li - I have some of them (Squidoo and Wizzley ones) set to pick up anything in the previous 24 hours that has the #hashtag #wizzley in or obviously #squidoo for the Squidoo one. So yes your tweet has to have the appropriate #hashtag in to get picked up and promoted
MiMi (Growwear) has one that picks up anything that has the #hashtag #newlens in the tweet as another example
You can also set them up by user - so you could have your own paper if you asked it to collate all your tweets into a newspaper - and there are various other options that I can't remember off the top of my head