Hood has beaten me to it

but as it was already compiled here is my take on the situation...
Whilst others have succeeded with using the TB6560 it is really not the best controller for the job. Just browsing this forum will show you the many problems some have experienced with this device and most of them have now moved on to something better, which works.
OK, it costs a bit more but bearing in mind the quality and support / backup that you will get I suggest that you consider something like the Gecko G540
http://www.geckodrive.com/catalogsearch/result/?q=540Gecko really do have a wealth of experience and the information available on their website is second to none.
Having said that and returning to your TB6560 problem – yes, your steppers should lock when power is applied so the problem may be with your Mach3 setup. Check that your X,Y and Z axis are enabled (Config / Ports and Pins / Motor Outputs) and that you have the correct port #1 address enabled – typically 0x378 (Port Setup and Axis Selection).
You need to be a bit wary because there are many, lack of knowledge / experience, errors on this website but there is some useful information regarding the TB6560 here
http://whatisacnc.com/driver-board/tb6560/In addition, you will also need to verify that the Mach3 license you purchased is valid license@machsupport.com as there have been a lot of fake licenses sold with the TB6560 boards and (from personal evaluation) they just do not work properly.
Tweakie.