The Port T bit could be set by either XGATE (not possible in your system), the CPU (does it write to that port?) or maybe by the timer (depending on how the system is configured).
The simplest approach for a dual-core system is to have them share access to as few common resurces as possible. This means that you don't have one waiting while the other performs its operation and in turn makes your system faster and more efficient.
If you do have to share resources then there are various approaches - have a look at the app note
AN2685.
I suggest you find out what is setting the bit first then decide if you can avoid this operation by moving the function to another port or by reassigning it to XGATE and if not then look at the ideas for sharing the port (including semaphores).
Don't forget that either core can cause an interrupt on the other and this can be used to force actions in response to system needs.