Sorry, this time stuff is something of a mess, and it's my fault. Well, sort of my fault....
When Teensy 3.0 came out, the Time library didn't work. It turns out there's a conflict between "time_t" in the library, and newlib's "time_t", which follows the POSIX standards. I exchanged several emails with Michael Margolis, author of the Time library. He preferred changing it to "atime_t". The Time library that comes with Teensyduino right now has that change.
Unfortunately, there are some other related Time libraries still using time_t. Also, it turns out there are quite a few people who feel very strongly about not changing the name. I'm starting to feel like the change was a mistake. I'm planning to revisit Time soon, probably putting it back to time_t. Someone recently suggested to me the possibility of using a "__time_t_defined" macro to automatically deal with the compatibility issues (where "automatically" is me writing a bunch of code so you never have to worry or even know about these issues).
So, first of all, I'm sorry this is such a mess. It's on my to-do list. So are lots of other things, and right now I'm finishing up a WS2811 LED library, so it'll be a while until I really work on this.
In the meantime, if you're using Teensy 2.0, the simplest thing to do is delete the Time library that came with Teensyduino (the one containing "atime_t", and replace it with the older copy found on the Arduino Playground. That should get you up and running.