I contacted Qualiteam and the answer is as follows:
<p class="ButtonsRow">{include file="buttons/button.tpl" button_title=$lng.lbl_open_new_window href="javascript
: window.open('https://www.mysite.com/home.php');" target="_blank" style="button"}</p>
i.e. change
href="https://www.mywebsite.com/home.php" target="_blank"
to
href="javascript
: window.open('https://www.mysite.com/home.php'); target="_blank"
Just thought I'd post up the answer in case anybody else ever had/has this problem.