The Browser mode in Blue Prism uses an Internet Explorer COM interface - so that will only work with Internet Explorer. Internet Explorer is a far more static/stable application to interface for enterprise RPA as it's COM api has been used by Blue Prism since IE 6, in that period Google is on it's third API. Also updates are easier to control.
If you really need to use Chrome or Firefox in v5 and the first versions of v6 your only option is to interface with it as a windows application, Accessibility Mode should be able to interact with most screen elements. On the roadmap is Microsoft UIA which will be better than Accessibilty mode (due out in Q1 2018) and Blue Prism is currently prototyping a new browser interface that will work with IE/Edge/Chrome/Firefox but is still in it's early development stages.