You did not provide a test file, but if you add enough text to start page 2, and the figure is small enough to be allowed at the top of a text page then it comes at teh top of page 2. I deleted [ht] as figure* can not be placed here.

\documentclass[twocolumn]{article}
\usepackage[utf8]{inputenc}
\usepackage{graphicx}
\usepackage{geometry}
\geometry{margin=1in}
\title{test}
\author{Pancake Senpai}
\date{September 2019}
\begin{document}
\maketitle
\section{Introduction}
This is a two column document and I want an image to spread across two
columns on the SECOND page. Rather than add a load of text here, I've kept
it short, but if you run this code then you should add a load of text so
that you're on page 2 before adding the image in order to replicate the
conditions.
\begin{figure*}
\centering
\includegraphics[width=\textwidth,height=5cm]{example-image}
\caption{My diagram.}
\end{figure*}
This is a two column document and I want an image to spread across two
columns on the SECOND page. Rather than add a load of text here, I've kept
it short, but if you run this code then you should add a load of text so
that you're on page 2 before adding the image in order to replicate the
conditions.
This is a two column document and I want an image to spread across two
columns on the SECOND page. Rather than add a load of text here, I've kept
it short, but if you run this code then you should add a load of text so
that you're on page 2 before adding the image in order to replicate the
conditions.
This is a two column document and I want an image to spread across two
columns on the SECOND page. Rather than add a load of text here, I've kept
it short, but if you run this code then you should add a load of text so
that you're on page 2 before adding the image in order to replicate the
conditions.
This is a two column document and I want an image to spread across two
columns on the SECOND page. Rather than add a load of text here, I've kept
it short, but if you run this code then you should add a load of text so
that you're on page 2 before adding the image in order to replicate the
conditions.
This is a two column document and I want an image to spread across two
columns on the SECOND page. Rather than add a load of text here, I've kept
it short, but if you run this code then you should add a load of text so
that you're on page 2 before adding the image in order to replicate the
conditions.
This is a two column document and I want an image to spread across two
columns on the SECOND page. Rather than add a load of text here, I've kept
it short, but if you run this code then you should add a load of text so
that you're on page 2 before adding the image in order to replicate the
conditions.
This is a two column document and I want an image to spread across two
columns on the SECOND page. Rather than add a load of text here, I've kept
it short, but if you run this code then you should add a load of text so
that you're on page 2 before adding the image in order to replicate the
conditions.
This is a two column document and I want an image to spread across two
columns on the SECOND page. Rather than add a load of text here, I've kept
it short, but if you run this code then you should add a load of text so
that you're on page 2 before adding the image in order to replicate the
conditions.
This is a two column document and I want an image to spread across two
columns on the SECOND page. Rather than add a load of text here, I've kept
it short, but if you run this code then you should add a load of text so
that you're on page 2 before adding the image in order to replicate the
conditions.
This is a two column document and I want an image to spread across two
columns on the SECOND page. Rather than add a load of text here, I've kept
it short, but if you run this code then you should add a load of text so
that you're on page 2 before adding the image in order to replicate the
conditions.
This is a two column document and I want an image to spread across two
columns on the SECOND page. Rather than add a load of text here, I've kept
it short, but if you run this code then you should add a load of text so
that you're on page 2 before adding the image in order to replicate the
conditions.
This is a two column document and I want an image to spread across two
columns on the SECOND page. Rather than add a load of text here, I've kept
it short, but if you run this code then you should add a load of text so
that you're on page 2 before adding the image in order to replicate the
conditions.
This is a two column document and I want an image to spread across two
columns on the SECOND page. Rather than add a load of text here, I've kept
it short, but if you run this code then you should add a load of text so
that you're on page 2 before adding the image in order to replicate the
conditions.
This is a two column document and I want an image to spread across two
columns on the SECOND page. Rather than add a load of text here, I've kept
it short, but if you run this code then you should add a load of text so
that you're on page 2 before adding the image in order to replicate the
conditions.
This is a two column document and I want an image to spread across two
columns on the SECOND page. Rather than add a load of text here, I've kept
it short, but if you run this code then you should add a load of text so
that you're on page 2 before adding the image in order to replicate the
conditions.
This is a two column document and I want an image to spread across two
columns on the SECOND page. Rather than add a load of text here, I've kept
it short, but if you run this code then you should add a load of text so
that you're on page 2 before adding the image in order to replicate the
conditions.
This is a two column document and I want an image to spread across two
columns on the SECOND page. Rather than add a load of text here, I've kept
it short, but if you run this code then you should add a load of text so
that you're on page 2 before adding the image in order to replicate the
conditions.
This is a two column document and I want an image to spread across two
columns on the SECOND page. Rather than add a load of text here, I've kept
it short, but if you run this code then you should add a load of text so
that you're on page 2 before adding the image in order to replicate the
conditions.
This is a two column document and I want an image to spread across two
columns on the SECOND page. Rather than add a load of text here, I've kept
it short, but if you run this code then you should add a load of text so
that you're on page 2 before adding the image in order to replicate the
conditions.
This is a two column document and I want an image to spread across two
columns on the SECOND page. Rather than add a load of text here, I've kept
it short, but if you run this code then you should add a load of text so
that you're on page 2 before adding the image in order to replicate the
conditions.
\end{document}
[ht](figure* can not dohso this just prevents float pages) alsofigure*comes at the earliest on the next page, so move it earliet in the source file. – David Carlisle Sep 10 '19 at 14:27example-imageas the image so that people can run it, but basically if the extra text is added after the figure I would expect that it works as you want – David Carlisle Sep 10 '19 at 14:28