WordPress wpdb->insert returns int(0) => doesn’t insert anything, no errors!

Your format is wrong.

On your code is should be

$insertion = $wpdb->insert($wpdb->prefix . 'table-name-of-plugin', array(
'column-name' => $stringValueForC1,
'second-column-name' => $stringValueForC2
    ), array('%s', '%s') );

Notice the change from

array('%s, %s')

to

array('%s', '%s')

Also, since you are setting the format for both of the value as string. I recommend that you just use

'%s'

The format parameter accepts either array or string. If it’s string, the string will be used as the format for all the values. Source – https://codex.wordpress.org/Class_Reference/wpdb#INSERT_row