Janeway would violate the Temporal Prime Directive if she did tell anything to Temporal Investigations.
Though I'm pretty sure that Temporal Investigations have an isolated “cleanroom” department that doesn't interact with the rest of the world to which people can confess experiences that would otherwise violate the Temporal PD, without that having any effect on history, which can then decide whether the information should be shared with anyone else or kept secret.
It would be interesting, however, what would be the status of that if this department was removed in 25th century, and no longer mentioned in the Temporal PD, and given that Braxton's XO told Janeway to share her experiences with no-one – did he take such change into account, and which version should Janeway ultimately follow?
And I think they might have violated the temporal PD by imprisoning Braxton earlier than they should have, but then again they probably don't really know if they did, and they would be also violating it if they didn't. I mean, they obviously messed with the time line in both cases, now whether that's enough to constitute a violation, I don't know.
P.S. The two guys from the department of TI are certainly in my list of “love at first sight” characters. And the look that Dax gave after their encounter was priceless. You certainly don't want to mess with them. I'm pretty sure that neither Ducane nor the alien helmsman would want to mess with them either, so 24th century wins!