Hi @dvize
If no checkbox value is selected, the get_field will return false. The in_array function expects an array, not false. This is why you see the error.
You need to write more bullet proof code like this:
$tours = get_field('tours');
<?php if ( !empty($tours) || !in_array( 'START wages-through-ages', get_field('tours') ) ) { ?>
my stuff
<?php } ?>