Hi,
I just used the timezone library with the ESP8266 platform and had problems due to conflicts with the xtensa time.h header that comes with the esp8266 compiler.
The solution (for me!) was to rename and edit the code as follows:
In the library directory for the Time library (.....\Arduino\libraries\Time)
Rename Time.h to TimeArd.h
In TimeArd.h change the include define to
#ifndef _TimeArd_h
#ifdef __cplusplus
#define _TimeArd_h
In Time.cpp change to #include "TimeArd.h"
In DateStrings.cpp change to #include "TimeArd.h"
It then compiled and worked fine.