The rule plainly states that "At the beginning of any turn in which Ku'gath is on the table (not including the one when he arrives from Reserve), the player may roll a dice....."
So, can he summon bases in the opposing player turn?
In the BRB it states on page 9, "Whenever a rule uses the word 'turn', both in this rule book and in Codexes, it means 'player turn', otherwise it will clearly state 'game turn'."
the codex wording just says 'turn' not 'game turn'
so he comes in on my turn 2. Best case scenario. On the opposing players turn, I can summon a base on a 4+.