How do I change the colours of the buttons on the event page?

You can change the colours of the buttons on the event details page by adding the following CSS codes under Calendar Settings > Customize > Custom CSS box:

.timely-nav>li>a {
background-color: #d8e3e9 !important;
}

.timely-nav>li.active>a {
background-color: #ec008c !important;
}

.timely-nav>li>a:hover {
background-color: #9dbfd2 !important;
}

.timely-nav>li.active>a:hover {
background-color: #ec008c !important;
}