I know that once you are in heat of the moment people tend to forget what actually happened and is happening outside of where they live. Although when you use safe, it can mean quite a lot of things, I would agree with you that, specifically to "Souther America" they are indeed safe, but due to very different reasons you imply.

They are "safer" not because they are not receiving immigrants, all of of the American continent is formed by immigrants, what happened is that recently the US decided to change it's policy, and stop being a nation of immigrants, while the rest of the continent haven't. A quick search will show you that, look at Shakira¹, the most famous Colombian singer, is of Arab descent, Carlos Slim Helú²³, the Mexican that is currently the second richest man on Earth, the same, and the biggest population of arabs living outside of the Arab world is in Brazil, with approximately 10 million Arab descendants⁴, while the US, in third, has about 3,5 million. And even with a far greater number of immigrants of the Arab countires than the US, they have none of the problems US has. So yes, "Souther America" is indeed safe, but it's because they treat immigrants and refugees as part of their population.

So, even better just to end this myth that "no other countries other then Europe and U.S. receive refugees or immigrants", take a look at the recent Haitian diaspora, that started, with greater speed, since the earthquake of 2010 in that country. Currently, there are more than 50 thousand Haitians living in Brazil⁵, which leads to an average of 10 thousand Haitians entering that country per year, which is 20% higher than that of the total of asylum seekers accepted in Germany⁶. But if you look at the amount of asylum seekers in the "Southern America" it's very low, because immigrants are strongly encouraged to not even ask for it, as more often than not the receiving country will just give them the paper they need to start working in the country, so they can as quickly as possible part of the nation. They are not treated as different, as people who need special care of the government. Usually NGOs help them in the beginning, so they adapt to their new country, but as soon as they want to call this new country their home they are welcomed as equal citizens.

tl;dr Immigration and refugees are happening all over the world, it's not a movement restricted to Europe and U.S. as you seem to imply. It's all a matter of how you decide to handle this movement, and quite honestly, it's just one more example of the failed Multiculturalism adopted by the EU. Oh, and just as a last tip, try not taking down governments and destabilize other countries, and you might actually get fewer immigrants.

Edit: the immigrant population and the rate that it increases in the US, is, to this day, very consistent to the historical average. I do believe that there is, as another user said, a myth that it's no longer an immigrant nation. I believe it's so because usually the opinions and comments you see are usually very hostile toward immigration, or in some cases also pretty radical in the other direction. I do stand corrected.