A process has been created that updates custom attributes (the attributes could even be on a custom object). The custom attributes are not updated until the page is refreshed.
This is working as designed.
Example: Idea converting to a Project
Note: Same logic applies to system action updates in the process.
Also note that, if there is an issue with modified values getting displayed in the UI, then it could be because of the UPDATE statements that are used in Gel Scripts. It is recommended to make use of the application's APIs - XOG and REST, instead of using direct UPDATE statements in scripts. These statements can encounter table locks and other issues in the DB, whereby the data remains unmodified.