Notifications don’t work correctly

After what someone has made an action (add post, vote and so on) notification does not change status instantly. Only then, what user refreshes the website. There is the same problem if a user wants to mark all notifications as seen. He gets the push message, that everything is ok “Successfully updated all notifications”, but the number of notifications stays the same. The user is forced to refresh the website and then is notifications clear.
It was tried at a new installation WordPress version 5.0.3 with only single plugin AnsPress Question Answer version 4.1.15 and template askbug version 3.1.9. We didn’t set any configuration and options.
Any idea what’s wrong?