Why does xcolor lighten a color when mixed

The xcolor package defines blue as a RGB color and cyan as a CMY color.

To make a mix, xcolor uses the color model of the first color and, if necessary, converts the second color.

To convert the CMY cyan to RGB cyan, you may add \colorlet{cyan}[rgb]{cyan} in your preamble.

\documentclass[tikz]{standalone}
\usepackage{tikz}
\colorlet{cyan}[rgb]{cyan}
\begin{document}
\begin{tikzpicture}
    \draw[cyan,fill=cyan] (0,0) rectangle (1,1);
    \draw[blue!0.5!cyan,fill=blue!0.5!cyan] (1,0) rectangle (2,1);
\end{tikzpicture}
\end{document}

Extract from xcolor manual (section 2.3.2 "Meaning of standard color expressions", p. 15, v2.11):

In general, the second color is transformed into the model of the first color then the mix is calculated within that model. Thus, name1!<percent>!name2 and name2!<100-percent>!name1 which should be equivalent theoretically, will not necessarily yield identical visual results.

Here is an example with three rows: default models, pure rgb model and pure cmy model.

\documentclass[tikz,margin=1mm]{standalone}
\usepackage[T1]{fontenc}
\usepackage{lmodern}
\usepackage{tikz}
\usetikzlibrary{positioning}

\colorlet{cmycyan}{cyan}
\colorlet{rgbcyan}[rgb]{cyan}

\colorlet{cmyblue}[cmy]{blue}
\colorlet{rgbblue}{blue}

\begin{document}
\begin{tikzpicture}
  \tikzset{
    block/.style 2 args={
      draw,right=-.5\pgflinewidth of a,
      fill=#1,text=#2,
      text height=.8em,text depth=.2em,text width=3.5cm,
      font=\ttfamily\bfseries,align=center,
    },
  }
  \node[anchor=base east] (a) {default models};
  \foreach \col/\txtcol in {blue/white,blue!1!cyan/black,cyan!99!blue/white,cyan/white}{
    \node[block={\col}{\txtcol}](a){\col};
  }

  \node[anchor=base east] (a) at (0,-1) {rgb model};
  \foreach \col/\txtcol in {rgbblue/white,rgbblue!1!rgbcyan/black,rgbcyan!99!rgbblue/black,rgbcyan/black}{
    \node[block={\col}{\txtcol}](a){\col};
  }

  \node[anchor=base east] (a) at (0,-2) {cmy model};
  \foreach \col/\txtcol in {cmyblue/white,cmyblue!1!cmycyan/white,cmycyan!99!cmyblue/white,cmycyan/white}{
    \node[block={\col}{\txtcol}](a){\col};
  }
\end{tikzpicture}
\end{document}

I don't know the details behind this, but blue!1!cyan is not the same as cyan!99!blue.

\documentclass[tikz]{standalone}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
    \filldraw[blue!1!cyan] (0,0) rectangle (-1,1);
    \filldraw[cyan] (0,0) rectangle (1,1);
    \filldraw[cyan!99!blue] (1,0) rectangle (2,1);
\end{tikzpicture}
\end{document}

No need to use \colorlet. You can also specify directly the color model of the mix ... but anyway macho programmers use only wavelengths. :)

\documentclass{article}
\usepackage{xcolor}
\begin{document}
\colorbox{rgb:blue!1!cyan,1}{}
\colorbox{rgb:cyan!99!blue,1}{}
\colorbox[wave]{480}{}
\colorbox{cmy:blue!1!cyan,1}{}
\colorbox{cmy:cyan!99!blue,1}{}
\end{document}