It is better, IMO, to annotate above math rather than include annotations as part of math. To this end, the tikzmark library can be used to mark some points to refer to them later when making your drawings.
\documentclass[12pt,a4paper]{article} \usepackage{amsmath} \usepackage{tikz} \usetikzlibrary{tikzmark} \begin{document} $\text{CI} = \bar{X}- z\tikzmark{p}_{\frac{\alpha}{2}} \frac{\sigma}{\sqrt{n}} < \mu < \bar{X}+z_{\frac{\alpha}{2}} \frac{\sigma}{\sqrt{n}} $ \tikz[overlay,remember picture]{% \draw[<->,dashed,red]([yshift=10pt]pic cs:p)--++(0,3ex)node[align=center,font=\tiny,black,above]{reliability\\ factor}; } \end{document}
If you still prefer your syntax, you can simply add \makebox[0pt]{<the picture>} and pull the math out of the node contents.
$\text{CI} =\bar{X}- z\makebox[0pt]{\tikz{\node(A406)[pin={[pin edge={red, dashed,<->},align=center,font=\tiny]90: reliability\\factor}]{};}} _{\frac{\alpha}{2}}\frac{\sigma}{\sqrt{n}} < \mu < \bar{X}+z_{\frac{\alpha}{2}} \frac{\sigma}{\sqrt{n}} $
The same result is obtained as above.
\documentclassto\end{document}.