Get ACF value after update user using Ajax

I’ve updated some ACF fields in user section via an ajax call using update_field() fonction.

update_field('field_name', 'field_value', 'user_' . $  user_id); 

When i take a look in the admin panel, everything is fine, but in front, i don’t have any values. In order to get those values i need to manualy save/update user in the back office.

In my template i use :

get_field('field_name','user_'.$  user_id); 

Any tips or advice ?

Thx in advance