Phase 10 - Who goes first?
In most rules given for the game it is stated that one player is chosen to be the dealer (source 1, source 2, source 3.) 
There is no mention of the dealer role going to another player in those.

Wikipedia says:
One player is chosen to be the dealer (alternately, the deal can rotate to the left after each hand).(source)
This seems to indicate that having the deal rotate is an alternate rule or houserule rather than an official rule.