I have discovered something more that might be a solution to more of these problems with time zones.
However, in Display tab in Global Settings for Display Units Time, I had set to UTC. It seems that was causing all the troubles with Tide importing and even with tracks importing. I have set this option to Local and now my Tides are importing (showing) correctly.
So, my conclusion would be: If you want to use time zones and not just the UTC time, this option needs to be set on Local!!!
Please Matt, correct me if I wrote it wrong!