Took a look at the 'tweets' view this module creates by default. It seems like it is taking uid in the argument. The defdault argument for uid is configured to take the uid from URL or take the node author's uid. So may be on pages where the above case doesn't provide the uid the block wont show.
I changed that to "display all values" if argument is not present, as I want only administer's tweets to be shown. Now the block shows up on the front page as it should.