Height of tcolorbox changed by g y p q

You need a \phantom of the character that makes the difference. I've chosen to put the same phantom (a tall and a deep character) in each box:

\documentclass{article}
\usepackage{tcolorbox}
\usepackage{multicol}
\begin{document}
    \begin{multicols}{2}
        \begin{tcolorbox}
            Hello\phantom{Hy}
        \end{tcolorbox}
        \columnbreak
        \begin{tcolorbox}
            Bye\phantom{Hy}
        \end{tcolorbox}
    \end{multicols}
\end{document}

Strictly speaking you can use \vphantom for a vertical correction, and probably should in this case. Even better is \strut, especially if you want to define your own new box:

\documentclass{article}
\usepackage{tcolorbox}
\newtcolorbox{oneliner}{fontupper=\strut}
\usepackage{multicol}
\begin{document}
    \begin{multicols}{2}
        \begin{oneliner}
            Hello
        \end{oneliner}
        \columnbreak
        \begin{oneliner}
            Bye
        \end{oneliner}
    \end{multicols}
\end{document}

Pages 15 and 29 of the tcolorbox manual explain how to make your own box, and the meaning of the various options. \vphantom{y} in place of \strut in the new box definitions doesn't work -- the phantom is set on one line and the real text underneath.

Another alternative is equal height group. All boxes from same group will have similar height (after two compilations), it doesn't matter if the are on same line or not.

\documentclass{article}
\usepackage{tcolorbox}
\usepackage{multicol}
\begin{document}
    \begin{multicols}{2}
        \begin{tcolorbox}[equal height group=A]
            Hello
        \end{tcolorbox}
        \columnbreak
        \begin{tcolorbox}[equal height group=A]
            Bye
        \end{tcolorbox}
    \end{multicols}
    \begin{multicols}{2}
        \begin{tcolorbox}[equal height group=A]
            aeo
        \end{tcolorbox}
        \columnbreak
        \begin{tcolorbox}
            aeo
        \end{tcolorbox}
    \end{multicols}
\end{document}

yet another workaround could be to use \strut:

\documentclass{article}
\usepackage{tcolorbox}
\usepackage{multicol}
\begin{document}
    \begin{multicols}{2}
        \begin{tcolorbox}
            \strut Hello
        \end{tcolorbox}
        \columnbreak
        \begin{tcolorbox}
            \strut Bye
        \end{tcolorbox}
    \end{multicols}
\end{document}