Thank you very much for your fast replies. I will post a picture of the power supply as soon as i’m home.
Jiggy-Ninja:
Did you have anything connected to the output of the boost module for this test?
Check the polarity of your input connections.He said it works on a battery, and breaks on the power supply. I think it’s more likely to be miswiring
Yes, I conmected the humidifier for this test and also double checked the polarity.
I know it would probably would have be better to test it with another load. But I have to add, that I also use this step up module for a PC fan on the same Power supply (Draws lower current).
jremington:
Step up modules have an input current limit, that you may not exceed. Consult the chip data sheet.
To produce 24V at 0.6A requires 12V at more than 1.2 A, taking into account conversion efficiency.
Like Jiggy-Ninja said it works with a 12V Battery. But it is close to the maximum rating, you’re right.
DVDdoug:
That’s a DC power supply, right? The humidifier may work with AC, but the DC-DC converter won’t.
And… If you’re using a power supply, get a 24V power supply (or a 24V transformer, since it will work on AC). A DC-DC voltage booster makes sense if you’re stuck with a battery, but if you’re using a power supply just use the right power supply. 
Sorry if I have not said it clearly. The humidifier works on AC and DC current. But thank you for your explication :).
TomGeorge:
Hi,
Welcome to the Forum.
Please read the first post in any forum entitled how to use this forum.
http://forum.arduino.cc/index.php/topic,148850.0.html
A picture or link to your 12V PSU would help, thanks.
Tom… 
I hope I have done nothing wrong. If so, please tell me and I try to make it better. I hope my english is not that bad and that you understand what I want to say. I’m from switzeland and still learning english in school^^.
Thank you again for your help. You have a really nice community:)
UPDATE
I’m home and added pictures from my power supply. I also should mention that the power supply works fine on a 3D Printer.

I also added a few pictures of my project, if you’re interested in for what I’m using this humidifier. It’s a Project that I’m working on for my graduation. The project is an automated greenhouse using a combination of an Arduino Mega, an Arduino Uno and a Raspberry Pi controlling irrigation, roof, fans and the humidifier:).