please try to change the icons at least once for all the content in customizer and then click publish.
if there is an image chooser there then please select images first and then add the content.
the changes will appear.
if these are not the case then please mail us your website link along with your wordpress username and password on [email protected] so we could check the issue. also in the mail if you could send a screenshot of the element which is not changing then it would be better for us to understand the issue so we could fix it quickly.