In good typography, the distance between two consecutive lines of text on a page should not depend on how tall the letters they contain are (well, this doesn’t hold true only in good typography!). For this reason, (La)TeX places their baselines at a fixed distance (for example, 12 points, or about 4.2mm), independently of the actual height of the glyphs inside. In this way, there is enough room to include, say, a math formula containing an exponent, or a \big parenthesis, in a line without having to move it vertically.
TeX implements this behavior by means of a mortar called “interline glue”, which is inserted between consecutive lines of text. In the implementation of \vspace*, special care is taken not to affect the way interline glue is inserted: this is usually correct, but, in your case, it has the side effect of positioning the first line of text as if it were taller than it actually is. This may or may not be what you want: if it is not, you can counteract it simply issuing the \nointerlineskip command, which suppresses the interline glue that would have normally been inserted before the line that immediately follows.
Note that, in the LaTeX implementation of \vspace*, the “interline glue” machinery adds over the “\topskip glue” appliance. More precisley, \vspace* adds an invisible horizontal rule to prevent the space it inserts from disappearing at a page break: now, setting \topskip to zero prevents unwanted vertical space from being inserted above this invisible rule; on the other hand, issuing the \nonterlineskip command prevents the interline glue (and hence, the vertical space it takes) from being added below the same rule. So, in your case, you need both.
MWE:
\documentclass[pagesize=auto, paper=102mm:49mm, paper=landscape]{scrartcl}
\usepackage[margin=3mm]{geometry}
% \showoutput
\begin{document}
\pagestyle{empty}
\setlength{\parindent}{0pt}
\setlength{\topskip}{0pt}
\nointerlineskip
\setlength{\parskip}{0pt}
\vspace*{\fill}
% \showthe\prevdepth
\begin{center}
Test
More tests
More tests
More tests
More tests
More tests
More tests
Test
\end{center}
\vspace*{\fill}
\end{document}
Setting \parskip to zero is not essential in this case, but it might be important in other contexts. Uncomment the commented lines to see some diagnostic messages.
\vspace*{\fill}and see if that works better – Raven Sep 01 '19 at 07:42\nointerlineskipat the very beginning of thecenterenvironment. – GuM Sep 01 '19 at 11:19