Both NVDA and JAWS can be configured to stay in one mode or the other unless the user changes it by intent using keyboard shortcuts. Both are also configured by default these days to switch from browse to forms mode when they land on a control during traversal and back to browse mode when they leave that control back to an area of straight text.
Gene has often mentioned that his personal preference is for "the old way" where the default was that you stayed in whatever mode you happen to be in until or unless you change it, no matter what you have landed on as you're making your way through the page.
It is odd that it would automatically switch to browse mode (or not leave browse mode) when landing on a control in the typical default configuration.
Brian - Windows 10 Home, 64-Bit, Version 1809, Build 17763
A great deal of intelligence can be invested in ignorance when the need for illusion is deep.
~ Saul Bellow, To Jerusalem and Back