"Stick with your strategy" is probably too dogmatic. What you always want to do is have a coherent strategy. What I mean by that is that I'm always picking up something that makes sense with what I have, as Davio suggests above. There are sometimes many things that make sense with your deck, and sometimes there are very few. But I am not going to be grabbing throne rooms after I have gone for a pretty action-bare BM strategy. And I'm probably not going to be grabbing coppers in my engine (though hey, depending on your engines, they can accept just about anything).
Indeed, there are lots of boards, particularly where there's lots of strong options and/or lots of interaction, where I will purposefully delay committing to any particular strategy in order to be able to react, and choose later, based on the strategy which my opponent is pursuing. The flexibility may be worse than "going for" any of the more straight-up strategies on the board, but it can still be better overall, because some strategies really counter others.
But trying to copy someone else's plan even four or five turns after they've started down that path, is usually a losing proposition, if you've committed hard to something else, or don't have any components that will help you out there. Four or five turns is a lot. Heck, two turns is substantial.