It states that you can move when the enemy ends its turn. At what point can the rogue use a reaction to move? I know it says when the turn ends but cant you use a reaction to interrupt another creatures turn...? 

My GM is playing it as we cant move until the creatures finishes his turn(basicly getting hit). It just doesn't seems as effective if the rogue is getting hit then moves. 

Thanks in advance! 

The rules:

Skirmisher

Starting at 3rd level, you are difficult to pin down during a fight. You can move up to half your speed as a reaction when an enemy ends its turn within 5 feet of you. This movement doesn’t provoke opportunity attacks.

Reactions

Certain special abilities, spells, and situations allow you to take a special action called a reaction. A reaction is an instant response to a trigger of some kind, which can occur on your turn or on someone else's. The opportunity attack, described later in this section, is the most common type of reaction.

When you take a reaction, you can't take another one until the start of your next turn. If the reaction interrupts another creature's turn, that creature can continue its turn right after the reaction.

The descripton of the ability tells you. When a creature ends their turn. Unless said other in the reaction trigger or feature text a reaction does not interrupt anything. Some do, like Shield spell can interrupt an attack, but others do not.

With Skirmisher it means if a creature ends their turn near you then you can move using your reaction.

Enemy 1 ends next to you. You use your reaction to move. Enemy 2's turn begins.

Thanks for clarifying it, I thought reaction allowed you to react at any time.