Try viewing the document with overprint preview on.
No that didnt change anything. My CMYK is set to US Web Coated (SWOP) v2 if that means anything.
To actually preview Neon colors just use your Neon monitor.
Neon colors are not within the range of colors an RGB model can produce. The swatches are a representation of a spot color which will be applied to the substrate you choose. In the case of your design I guess this would be T-Shirts. If you invent a Neon monitor and want to work on a design with Neon colors for any length of time you might want to put on sunglasses. Makes my eyes hurt just thinking about it.
Command+Shift+Option+Y toggles this preview mode.
And you say this changed nothing?
When I put a big swatch of color and color it as 804 yes it looks pastel until I switch to overprint preview. Then it only gets a bit darker and oranger. Still no real way for you to softproof any Neon colors.
Neon colours cannot be made from CMYK. You need spot colours.
As the others said, there is no way to preview this on a monitor. Just define the spot colors properly in the document and hand it over to the textile printer. If he knows what a Pantone swatch is, he will pick the right colors. If he uses some other concoctions based on a textile specific color system, he will call you up, anyway, and you will have to sort this out on the location. Also make sure you get things right with any additional layers of white underprint or special additional reflective pigment., depending on how brigh tyou want your dayglo orange or whatever...