The definition changes from situation to situation based on what is most convenient to those with the upper hand where the "refugee" is involved.
At its core, a refugee is a player coming out of the bad side of a war, either being targeted or to be targeted as the other tribe assumes victory, but in reality a refugee is only a refugee for as long as a tribe is willing to chase them. If you find a player who has held his own, has gained experience and is worth trying to bring in, then you take that gamble and risk bringing the war to your door. As you can imagine this goes one of two ways, the other tribe pushes forward on its momentum and continues the war to a new tribe as it chases the refugees, or it backs down, albeit while holding onto a grudge for the insult.
Either way, when the word refugee gets thrown around, diplomacies get called into question and each tribe involved must choose whether it will stick to its guns or move on.
Generally I find that the more hassle, the more of a threat, the "refugee" is to the tribe, then the more they will push and flex to try and out him on his own so that they might take him down while he has no tribe to call at his back.
This is my opinion, and your question is one of GREAT opinion since there are no set rules for it in this game.