I think it might issue at code.
The data for the welcome message section coming from customer-data
.In order to understand it, you have to check how Private content worked on Magento 2.
Study the links:
The data for private content like cart, customer data is stored at local storage of your browser and data has come from an Ajax reqest at www.example.com/customer/section/load/
.
If 5mins take time to get response from this URL it means some customization will make delay on reponse from this Url.
So, you have to debug it and fix it by checking everysection.xml