Advanced searches on Startpage, including exact match, perform the same as on Google and Bing, which is to say that they work, but are not applied in 100% of searches. More information can be found here:

https://support.startpage.com/hc/en-us/articles/4521473758228-Advanced-Search-on-Startpage

If you wish to discuss anything further, feel free to reach out at support@startpage.com. Thanks for caring about privacy.