Is this online fluorophore database reliable?
That is the correct domain name for the respected and accredited University of Arizona. I would feel confident using their data.

In general, that's the key: being certain that the source is who they say they are, and that they are a source that you have some reason to trust.  

Regarding security, it's unlikely someone would spend the time, money and effort required to falsify some fluorescence spectra database.  If it were a database of controversial climate data, or clinical trials for a new medication, etc., you might want to investigate what the site does to secure their data.  

I would also be cautious of using open wiki data like Wikipedia. Although I've personally gotten into the habit of trusting those sites more than I should, anybody can edit them. And while they try to police the sites for poorly documented data and such, it's a lot to keep up with. A good wiki article will have sources for their data, and reaching out directly to the source, if possible, is the better way of getting reliable data from a wiki site.