How to prepopulate a term reference field with multiple values on a new form?
Answering my own question:
1) First aspect is to feed the data correctly to the term reference field. The magic formula I found is:

$form['field_revactivities'][LANGUAGE_NONE]['#default_value'] = array($bidule);


where $bidule is a the string of taxonomy term (not its taxonomy id).

2) If there are multiple elements in the field_ad_tags, then I had to create a loop to place them all one after the other in a string. It was important to have the exact wording of each taxonomy term for the field to recognise which tag it is and to separate them with a comma. Here is my final code:

$bidule = '';
$i=0;
foreach ($node-&gt;field_ad_tags['und'] as $truc =&gt; $value) {
        drupal_set_message('&lt;pre&gt;$truc '. print_r($value, TRUE) .'&lt;/pre&gt;');
        $term = taxonomy_term_load($node-&gt;field_ad_tags['und'][$i]['tid']);
        $name = $term-&gt;name;
        $bidule= $bidule.','.$name;
        $i++;
}
$bidule=substr($bidule, 1); // Remove the first character ','

$form['field_revactivities'][LANGUAGE_NONE]['#default_value'] = array($bidule);