No. Many in the Global South actually do believe that western superpowers create unrest in poor and developing countries to weaken them and exploit their resources which also include human resources.
While I don't believe that Western Europe caused wars in the Middle East for cheap labour / increased birthrate, I do see how big European corporations massively benefit from having a large influx of refugees. They do the jobs that natives don't want to do anymore. If you are looking for a garbage collector, a native will likely want 150% of minimum wage for that job. A recent refugee eager to start working has no problem doing the same job for minimum wage and zero benefits.
You are missing the big picture - blue collar workers can be easily attracted from anywhere in the world. War and unrest also causes the rich and the educated to seek opportunities elsewhere, and these are often the kind of people who also have the means to find opportunities abroad more easily. Getting a young, qualified and educated person as a refugee is huge bonus because without spending a dime on them you are getting a potentially productive tax payer and prospective citizen. And often these educated refugees are willing to do blue collar work too. You are right though that the middle-eastern conflicts aren't primarily about cheap labour but oil. Everything else is just the secondary benefit.