Twitterrific doesn't save my last read tweet I'm giving Twitterrfic a test drive. I'm not sure about the issue but it looks to me the Twitterrfic doesn't keep my last read tweet after a relaunch.
I mean Nambu and Twitter official client save my last read tweet, thus I can scroll through all the new tweets. Twitterrific scrolls me to the newest tweet.
I can't read the tweets while I'm offline.  

Any way to make Twitterrfic behaves like Nambu or Twitter?
Two possible things happening here. 

1) You have "Always scroll to top" turned on in Twitterrific's prefs. Head to the settings app to check and make sure it's turned off.

2) You're receiving more tweets than the timeline can hold and so your previous reading position is "off the timeline". When this happens, Twitterrific defaults to the top of the timeline (the most recent tweet).

This is changing in the 4.1.1 update however so that even if you receive more tweets than the timeline holds, it will take you to the bottom instead of the top.

Hope this helps.