Can a Rummikub tile be moved
During your turn, you can pretty much do whatever you see fit with every tile on the table, including those you've only just placed. As long as the end result has no invalid sets. Except, apparently, joker tiles:

From Rummikub.org:


  With the exception of the joker, any tile on the table may be repositioned provided that all tiles on the board eventually become part of a meld. The joker may be used in place of any tile when forming melds, but once a joker is on the table it cannot be moved to another meld. It must first be replaced by the tile for which it was used. 


I cite this source, because it seems to be the most reliable one. But, truthfully, I wasn't aware of the joker exception.