ESI created block is not purged

we are working with litespeed enterprise and ESI to optimize our caching. 

The caching it self is now working:

// emit the cache esi tag
$param['id'] = 12345;
echo apply_filters(
            'litespeed_esi_url',
            'priceblock',
            'price',
            $param,
            'private,no-vary',
            false,
            true,
            true,
            $param );

// process the esi tag 
add_action( 'litespeed_esi_load-priceblock', 'esi_priceblock' );
function esi_priceblock($att) {
    // here is the problem
    do_action( 'litespeed_tag_private_esi', 'tag_price' );
    do_action( 'litespeed_tag_add', 'tagprice2' );
    
    do_action( 'litespeed_control_set_ttl', 600 );

    echo "Some Data to be cached " . date("r");
}

The implementation above is working as is should, now I would like to expired the block.
So what we tried was (where actually nothing worked):

1) purge
do_action( 'litespeed_purge', 'tag_price' );
do_action( 'litespeed_purge', 'tagprice2' );  
do_action( 'litespeed_purge', 'priceblock' );

2) using litespeed_purge_esi
3) using litespeed_purge_private_esi
4) litespeed_purge_widget

all of these which the different names (tag_price, tagprice2, priceblock)

Then we added also: 
do_action( 'litespeed_purge_finalize');
But also this did not change anything.

So howto expire the block, by using one of the above names ? Or maybe the data has to be marked in somewhat another way / function ?

best

CHA