It is more than 10%. It depends on how much food is missing to feed everybody. After the rush I had like 23 pops needing food (the two other being the colonizing synth and the one I started to build just as the colony was created). It was a tomb world that I terraformed. It had plenty of research bonuses but no food tile *at all*. As soon as I colonized I built a space station and orbital hydroponics. Yet, after the rush it got to like "-14" food, with a happiness hit of about 70%. Mind you, my empire is quite happy, but everybody got their happiness to zero.
It is not critical, in fact, I found it funny. But there should be a way to counter that. IMO migration is quite broken... Having core worlds filled with pops that won't migrate because they are happy, yet have food surplus... If someone does migrate it leaves a hole and needs to grow again, even if it has had decades of food surplus. I don't think it makes sense.
Even if I don't like the idea of a single pool for food, maybe it should be possible to funnel food to a specific planet (an edict maybe?). Maybe have migration to be accounted in the new planet while migrating and abort if no food is available (that could be optional anyways).
In any case, picture the arrival of enough people to fill a huge planet... all at once.