Great question. Yes that seems normal. I have heard of many PM's taking a month (or half a month) for placing a tenant. This money is earned. Advertising, screening, showing the property etc.
However, while I think the PM earns their money the tenant placement fee is the main reason I do not have a PM. I am okay with the monthly management fee. If you have one or two units this will often be 10%, as you have more and more nits this percentage will go down. I have a couple PM companies offering me 7% since I have 11 units.
The problem is having different goals. A landlord wants as little turn over as is possible. (At least that is my goal) With my criteria I have had one turnover, and that is because she inherited a house. A PM company makes money on turn over, so while many say they want no turnover I am hesitant to put my properties in the hands of someone who would benefit from my expenses going up.
So while I plan on having a PM in AZ I will be shopping around for a low fixed rate placement fee, even if that means I pay a percent or so more in monthly fees. This way our goals would be more aligned.