It depends dramatically on two things:
1. the type of time travel in effect. I'll assume Marvel-flavor time travel, where going back is really jumping to a different universe that shares the same history till the arrival time. But if it's something more complicated then relaying info back might Marty McFade the prognosticator out of existence.
2. the level of information available to the prognosticator (future communicator). Is it near-total, so they could tell the recipient to "duck… now!" or is it just public info like stock prices, weather, and what's on the news?
Best case for the recipient is that for each change they make, they still have an ally relaying valuable info from the future that includes those changes. And also that said ally has near-total information to help protect the recipient.
Worst case for the recipient is that after they make one change, they are now in a timeline where their future ally no longer communicates with them. This is also the most detectable for others in the recipient's time because the recipient will likely make some big bets based on the one-shot info they receive, and won't have additional info to help avoid detection.
To continue the thought experiment: if you developed that technology in the year 2120, how would you use it, and would that be detectable in the year 2020?