And on top of that, the asylum seekers are very unevenly divided between the EU countries.
I actually made a note of that in my post
For example in Finland, at the moment the average number of persons coming to the country is several hundreds a day, even though we are about the most distant country. You can compare to the birth rate which is about 150 babies a day. And you have to multiply that number because of family reunions. At this speed Finns are going to be minority in Islamic country within relative short time even if the immigrants didn't make any babies and much faster as in reality they too make babies.
I think you need to redo the math on that. Let us say that "several hundred" is 300, so the number of new people in Finland is 450 per day. Finland has a population of 5.5 million, so it would take 5.5e6/300 ~= 18000 days ~= 50 years at the current rate of immigration for there to be as many migrants as there are Fins.
Germany alone expects up to 1.5 million asylum seekers this year. And the next year is probably going to be worse as the number of asylum seekers wasn't as high at the beginning of this year, but the flow of asylum seekers has been constantly accelerating.
And Turkey, which has a similar population as Germany but is a lot poorer, has taken 2 million. Lebanon and Jordan has taken 1 million each. There is also a limitation on the number of refugees. The population of Syria was 22 million before the war started, 5-6 million of whom have fled the country. Even assuming that the entire Syrian population is fleeing to EU (which is quite unlikely), we are looking at 4% increase in the EU population. In my world, that is a manageable population increase if EU actually manages to get its shit together.